Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Textbook Question
Chapter 4.7, Problem 5E
In Problems 1–18 solve the given differential equation.
5. x2y″ + xy′ + 4y = 0
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Chapter 4 Solutions
Differential Equations with Boundary-Value Problems
Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Prob. 7ECh. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...
Ch. 4.1 - (a) Use the family in Problem 1 to find a solution...Ch. 4.1 - Prob. 12ECh. 4.1 - In Problems 13 and 14 the given two-parameter...Ch. 4.1 - In Problems 13 and 14 the given two-parameter...Ch. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - Prob. 20ECh. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - In Problems 1522 determine whether the given set...Ch. 4.1 - In Problems 2330 verify that the given functions...Ch. 4.1 - Prob. 24ECh. 4.1 - In Problems 2330 verify that the given functions...Ch. 4.1 - In Problems 2330 verify that the given functions...Ch. 4.1 - In Problems 2330 verify that the given functions...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - In Problems 2330 verify that the given functions...Ch. 4.1 - In Problems 31–34 verify that the given...Ch. 4.1 - Prob. 32ECh. 4.1 - In Problems 3134 verify that the given...Ch. 4.1 - In Problems 31–34 verify that the given...Ch. 4.1 - (a) Verify that and are, respectively, particular...Ch. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Suppose that y1 = ex and y2 = ex are two solutions...Ch. 4.1 - (a) Verify that y1 = x3 and y2 = |x|3 are linearly...Ch. 4.1 - Is the set of functions f1(x) = ex+2, f2(x) = ex3...Ch. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - Prob. 6ECh. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 116 the indicated function y1(x) is a...Ch. 4.2 - In Problems 1720 the indicated function y1(x) is a...Ch. 4.2 - In Problems 1720 the indicated function y1(x) is a...Ch. 4.2 - In Problems 1720 the indicated function y1(x) is a...Ch. 4.2 - In Problems 1720 the indicated function y1(x) is a...Ch. 4.2 - Prob. 21ECh. 4.2 - In Problems 21 and 22 the indicated function y1(x)...Ch. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.3 - In Problems 114 find the general solution of the...Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - In Problems 114 find the general solution of the...Ch. 4.3 - Prob. 8ECh. 4.3 - In Problems 114 find the general solution of the...Ch. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - In Problems 114 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - Prob. 20ECh. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - Prob. 22ECh. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - In Problems 1528 find the general solution of the...Ch. 4.3 - Prob. 28ECh. 4.3 - In Problems 2936 solve the given initial-value...Ch. 4.3 - In Problems 2936 solve the given initial-value...Ch. 4.3 - In Problems 2936 solve the given initial-value...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - In Problems 3740 solve the given boundary-value...Ch. 4.3 - In Problems 41 and 42 solve the given problem...Ch. 4.3 - In Problems 41 and 42 solve the given problem...Ch. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - In Problems 4958 find a homogeneous linear...Ch. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Two roots of a cubic auxiliary equation with real...Ch. 4.3 - Find the general solution of 2 + 7y + 4y 4y 0 if...Ch. 4.3 - Find the general solution of y + 6y + y 34y = 0...Ch. 4.3 - To solve y(4) + y = 0, we must find the roots of...Ch. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - Prob. 9ECh. 4.4 - In Problems 1–26 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - Prob. 12ECh. 4.4 - In Problems 1–26 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - Prob. 20ECh. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - In Problems 126 solve the given differential...Ch. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - In Problems 2736 solve the given initial-value...Ch. 4.4 - In Problems 2736 solve the given initial-value...Ch. 4.4 - Prob. 32ECh. 4.4 - In Problems 2736 solve the given initial-value...Ch. 4.4 - In Problems 2736 solve the given initial-value...Ch. 4.4 - In Problems 2736 solve the given initial-value...Ch. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - In Problems 3740 solve the given boundary-value...Ch. 4.4 - Prob. 39ECh. 4.4 - In Problems 3740 solve the given boundary-value...Ch. 4.4 - In Problems 41 and 42 solve the given...Ch. 4.4 - In Problems 41 and 42 solve the given...Ch. 4.4 - Consider the differential equation ay + by + cy =...Ch. 4.4 - Prob. 44ECh. 4.4 - In Problems 4548 without solving, match a solution...Ch. 4.4 - In Problems 4548 without solving, match a solution...Ch. 4.4 - In Problems 4548 without solving, match a solution...Ch. 4.4 - Prob. 48ECh. 4.5 - In Problems 110 write the given differential...Ch. 4.5 - In Problems 110 write the given differential...Ch. 4.5 - In Problems 110 write the given differential...Ch. 4.5 - Prob. 4ECh. 4.5 - In Problems 110 write the given differential...Ch. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - In Problems 110 write the given differential...Ch. 4.5 - In Problems 110 write the given differential...Ch. 4.5 - In Problems 1114 verify that the given...Ch. 4.5 - In Problems 1114 verify that the given...Ch. 4.5 - In Problems 11-14 verify that the given...Ch. 4.5 - In Problems 11-14 verify that the given...Ch. 4.5 - In Problems 15-26 find a linear differential...Ch. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - In Problems 15-26 find a linear differential...Ch. 4.5 - In Problems 1526 find a linear differential...Ch. 4.5 - Prob. 23ECh. 4.5 - In Problems 1526 find a linear differential...Ch. 4.5 - In Problems 1526 find a linear differential...Ch. 4.5 - In Problems 1526 find a linear differential...Ch. 4.5 - In Problems 27-34 find linearly independent...Ch. 4.5 - In Problems 27-34 find linearly independent...Ch. 4.5 - In Problems 27-34 find linearly independent...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - In Problems 2734 find linearly independent...Ch. 4.5 - Prob. 34ECh. 4.5 - In Problems 35-64 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - In Problems 35-64 solve the given differential...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - In Problems 3564 solve the given differential...Ch. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - In Problems 6572 solve the given initial-value...Ch. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.6 - In Problems 118 solve each differential equation...Ch. 4.6 - In Problems 118 solve each differential equation...Ch. 4.6 - In Problems 118 solve each differential equation...Ch. 4.6 - Prob. 4ECh. 4.6 - In Problems 1-18 solve each differential equation...Ch. 4.6 - Prob. 6ECh. 4.6 - In Problems 1-18 solve each differential equation...Ch. 4.6 - In Problems 118 solve each differential equation...Ch. 4.6 - In Problems 118 solve each differential equation...Ch. 4.6 - In Problems 118 solve each differential equation...Ch. 4.6 - Prob. 11ECh. 4.6 - Prob. 12ECh. 4.6 - In Problems 1-18 solve each differential equation...Ch. 4.6 - In Problems 1-18 solve each differential equation...Ch. 4.6 - In Problems 1-18 solve each differential equation...Ch. 4.6 - Prob. 16ECh. 4.6 - In Problems 1-18 solve each differential equation...Ch. 4.6 - Prob. 18ECh. 4.6 - In Problems 19-22 solve each differential equation...Ch. 4.6 - In Problems 19-22 solve each differential equation...Ch. 4.6 - In Problems 19-22 solve each differential equation...Ch. 4.6 - In Problems 19-22 solve each differential equation...Ch. 4.6 - Prob. 23ECh. 4.6 - In Problems 23-26 proceed as in Example 3 and...Ch. 4.6 - In Problems 23-26 proceed as in Example 3 and...Ch. 4.6 - In Problems 23-26 proceed as in Example 3 and...Ch. 4.6 - In Problems 27 and 28 the indicated functions are...Ch. 4.6 - In Problems 27 and 28 the indicated functions are...Ch. 4.6 - Prob. 29ECh. 4.6 - In Problems 2932 solve the given third-order...Ch. 4.6 - Prob. 31ECh. 4.6 - Prob. 32ECh. 4.6 - In Problems 33 and 34 discuss how the methods of...Ch. 4.6 - Prob. 34ECh. 4.6 - Prob. 35ECh. 4.6 - Find the general solution of x4y+x3y4x2y=1 given...Ch. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - Prob. 6ECh. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - Prob. 8ECh. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - In Problems 118 solve the given differential...Ch. 4.7 - Prob. 18ECh. 4.7 - In Problems 19-24 solve the given partial equation...Ch. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - In Problems 19-24 solve the given partial equation...Ch. 4.7 - In Problems 1924 solve the given differential...Ch. 4.7 - In Problems 2530 solve the given initial-value...Ch. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - In Problems 25-30 solve the given initial-value...Ch. 4.7 - Prob. 29ECh. 4.7 - In Problems 25-30 solve the given initial-value...Ch. 4.7 - In Problems 3136 use the substitution x = et to...Ch. 4.7 - Prob. 32ECh. 4.7 - In Problems 3136 use the substitution x = et to...Ch. 4.7 - In Problems 3136 use the substitution x = et to...Ch. 4.7 - Prob. 35ECh. 4.7 - In Problems 3136 use the substitution x = et to...Ch. 4.7 - Prob. 37ECh. 4.7 - In Problems 37 and 38 use the substitution t = x...Ch. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - Prob. 42ECh. 4.7 - Prob. 43ECh. 4.7 - Prob. 44ECh. 4.7 - Prob. 45ECh. 4.7 - Prob. 46ECh. 4.7 - Bending of a Circular Plate In the analysis of the...Ch. 4.7 - Prob. 48ECh. 4.8 - In Problems 16 proceed as in Example 1 to find a...Ch. 4.8 - In Problems 16 proceed as in Example 1 to find a...Ch. 4.8 - Prob. 3ECh. 4.8 - Prob. 4ECh. 4.8 - Prob. 5ECh. 4.8 - Prob. 6ECh. 4.8 - Prob. 7ECh. 4.8 - In Problems 712 proceed as in Example 2 to find...Ch. 4.8 - Prob. 9ECh. 4.8 - Prob. 10ECh. 4.8 - Prob. 11ECh. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.8 - In Problems 13-18 proceed as in Example 3 to find...Ch. 4.8 - Prob. 19ECh. 4.8 - Prob. 20ECh. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - In Problems 19-30 proceed as in Example 5 to find...Ch. 4.8 - Prob. 24ECh. 4.8 - Prob. 25ECh. 4.8 - Prob. 26ECh. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.8 - Prob. 30ECh. 4.8 - Prob. 31ECh. 4.8 - In Problems 31-34 proceed as in Example 6 to find...Ch. 4.8 - Prob. 33ECh. 4.8 - Prob. 34ECh. 4.8 - Prob. 35ECh. 4.8 - Prob. 36ECh. 4.8 - Prob. 37ECh. 4.8 - Prob. 38ECh. 4.8 - Prob. 39ECh. 4.8 - Prob. 40ECh. 4.8 - Prob. 41ECh. 4.8 - In Problems 39-44 proceed as in Examples 7 and 8...Ch. 4.8 - Prob. 43ECh. 4.8 - Prob. 44ECh. 4.9 - In Problems 120 solve the given system of...Ch. 4.9 - Prob. 2ECh. 4.9 - Prob. 3ECh. 4.9 - Prob. 4ECh. 4.9 - Prob. 5ECh. 4.9 - Prob. 6ECh. 4.9 - Prob. 7ECh. 4.9 - In Problems 120 solve the given system of...Ch. 4.9 - Prob. 9ECh. 4.9 - Prob. 10ECh. 4.9 - Prob. 11ECh. 4.9 - Prob. 12ECh. 4.9 - Prob. 13ECh. 4.9 - Prob. 14ECh. 4.9 - Prob. 15ECh. 4.9 - Prob. 16ECh. 4.9 - Prob. 17ECh. 4.9 - In Problems 120 solve the given system of...Ch. 4.9 - Prob. 19ECh. 4.9 - Prob. 20ECh. 4.9 - Prob. 21ECh. 4.9 - Prob. 22ECh. 4.9 - Projectile Motion A projectile shot from a gun has...Ch. 4.9 - Prob. 24ECh. 4.9 - Prob. 25ECh. 4.10 - Prob. 1ECh. 4.10 - Prob. 2ECh. 4.10 - In Problems 3-6 the dependent variable y is...Ch. 4.10 - Prob. 4ECh. 4.10 - In Problems 3-6 the dependent variable y is...Ch. 4.10 - Prob. 6ECh. 4.10 - In Problems 710 the independent variable x is...Ch. 4.10 - Prob. 8ECh. 4.10 - Prob. 9ECh. 4.10 - Prob. 10ECh. 4.10 - Prob. 11ECh. 4.10 - In Problems 11 and 12 solve the given...Ch. 4.10 - Prob. 13ECh. 4.10 - Prob. 14ECh. 4.10 - Prob. 15ECh. 4.10 - In Problems 15 and 16 show that the substitution u...Ch. 4.10 - In Problems 17–20 proceed as in Example 3 and...Ch. 4.10 - Prob. 18ECh. 4.10 - Prob. 19ECh. 4.10 - Prob. 20ECh. 4.10 - In calculus the curvature of a curve that is...Ch. 4.10 - Prob. 22ECh. 4.10 - Discuss how the method of reduction of order...Ch. 4.10 - Prob. 24ECh. 4.10 - Prob. 25ECh. 4 - Answer Problems 110 without referring back to the...Ch. 4 - Answer Problems 110 without referring back to the...Ch. 4 - Answer Problems 110 without referring back to the...Ch. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - If y1 = ex and y2 = ex are solutions of...Ch. 4 - Prob. 11RECh. 4 - Without the aid of the Wronskian, determine...Ch. 4 - Suppose m1 = 3, m2 = 5, and m3 = 1 are roots of...Ch. 4 - Prob. 14RECh. 4 - In Problems 15 and 16 find a homogeneous...Ch. 4 - Prob. 16RECh. 4 - In Problems 1732 use the procedures developed in...Ch. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - In Problems 1732 use the procedures developed in...Ch. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - In Problems 33 and 34 write down the form of the...Ch. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - In Problems 47-50 use systematic elimination to...Ch. 4 - Prob. 49RECh. 4 - Prob. 50RE
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- A horse trainer teaches horses to jump by using two methods of instruction. Horses being taught by method A have a lead horse that accompanies each jump. Horses being taught by method B have no lead horse. The table shows the number of training sessions required before each horse performed the jumps properly. Method A 25 23 39 29 37 20 Method B 41 21 46 42 24 44 Method A 45 35 27 31 34 49 Method B 26 43 47 32 40 Use a rank-sum test with a5% level of significance to test the claim that there is no difference between the training sessions distributions. If the value of the sample test statistic R, the rank-sum, is 150, calculate the P-value. Round your answer to four decimal places.arrow_forwardA data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales. Person 1 2 3 4 5 6 x rank 8 11 2 4 5 3 y rank 7 10 1 3 2 4 Person 7 8 9 10 11 x rank 7 9 10 1 6 y rank 8 11 9 6 5 Using a 1% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Verify that the Spearman rank correlation coefficient . This implies that the P-value lies between 0.002 and 0.01. State…arrow_forwardSand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2? arrow_forward
- Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2?arrow_forward29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forwardSand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 27.3 34.6 30.6 27.8 33.4 31.5 27.3 31.2 32.0 24.7 24.4 28.2 Test this sequence for randomness about the median. Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives BAABAABAABBB. Verify that the number of runs is 7, the lower critical number is 3, and the upper critical number is 11. Use a 5% level of significance. State the conclusion of the test and interpret your results.arrow_forward
- 29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.arrow_forward3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.arrow_forward
- 2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forwardPlease solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forward
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