DIFFERENTIAL EQUATIONS-ACCESS
4th Edition
ISBN: 9781133109044
Author: Blanchard, Devaney, and Hall
Publisher: ACME
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Chapter 3.2, Problem 15E
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Stat questions
1)
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let Xt is stochastic process with WSS
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1) E (X5) = \ 1
2
Show that
E (X5 = X 3 = 2 (= = =)
Since X is WSSEL
2
3) find E(X5+ X3)²
4) sind E(X5+X2) J=1
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Question 1: Let X be a random variable with p.m.f
(|x| +1)²
x= -2, -1, 0, 1,2
f(x) =
C
0,
O.W
1. The value of c.
2. The c.d.f.
3. E(X).
4. E(2x+3).
5. E(X²).
6. E(3x²+4).
7. E(X(3X+4)).
8. Var(X).
9. Var (6-3X).
10. Find the m.g.f of the random variable X
Chapter 3 Solutions
DIFFERENTIAL EQUATIONS-ACCESS
Ch. 3.1 - Recall the model dx dt=ax+by dy dt=cx+dy for...Ch. 3.1 - In Exercises 57 , rewrite the specified linear...Ch. 3.1 - In Exercises 57 , rewrite the specified linear...Ch. 3.1 - In Exercises 57 , rewrite the specified linear...Ch. 3.1 - In Exercises 89 , rewrite the specified linear...Ch. 3.1 - For the linear systems given in Exercises 1013,...Ch. 3.1 - For the linear systems given in Exercises 1013,...Ch. 3.1 - Prob. 13ECh. 3.1 - Let A=(abcd) be a nonzero matrix. That is, suppose...Ch. 3.1 - The general form of a linear, homogeneous,...
Ch. 3.1 - Convert the third-order differential equation $...Ch. 3.1 - Consider the linear system dYdt=(2011)Y Show that...Ch. 3.1 - Consider the linear system dYdt=(1 113)Y (a)Show...Ch. 3.1 - A=( 2 33 2) Functions: Y1(t)=e2t(cos3t,sin3t)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises 110 (a) compute the eigenvalues; (b)...Ch. 3.2 - In Exercises $1-10$ (a) compute the eigenvalues;...Ch. 3.2 - Solve the initial-value problem dx dt=2x2y dy...Ch. 3.2 - Solve the initial-value problem dYdt=( 412...Ch. 3.2 - Show that a is the only eigenvalue and that every...Ch. 3.2 - A matrix of the form A=(ab0d) is called upper...Ch. 3.2 - A matrix of the form B=(abbd) is called symmetric....Ch. 3.2 - Consider the second-order equation...Ch. 3.2 - For the harmonic oscillator with mass m=1, spring...Ch. 3.2 - In Exercises 21-24, we return to Exercises 1-4 in...Ch. 3.3 - In Exercises 18, we refer to linear systems from...Ch. 3.3 - In Exercises 18, we refer to linear systems from...Ch. 3.3 - In Exercises 18, we refer to linear systems from...Ch. 3.3 - In Exercises 1-8, we refer to linear systems from...Ch. 3.3 - In Exercises 912, we refer to initial-value...Ch. 3.3 - In Exercises 13-16, we refer to the second-order...Ch. 3.3 - The slope field for the system dx dt=2x+12y dy...Ch. 3.3 - Consider the linear system dYdt=( 2102)Y $ (a)...Ch. 3.4 - Suppose that the 22 matrix A has =1+3i as an...Ch. 3.4 - Suppose that the 22 matrix B has =2+5i as an...Ch. 3.4 - In Exercises 3-8, each linear system has complex...Ch. 3.4 - In Exercises 3-8, each linear system has complex...Ch. 3.4 - In Exercises 3-8, each linear system has complex...Ch. 3.4 - In Exercises 3-8, each linear system has complex...Ch. 3.4 - In Exercises 3-8, each linear system has complex...Ch. 3.4 - In Exercises 9-14, the linear systems are the same...Ch. 3.4 - In Exercises 9-14, the linear systems are the same...Ch. 3.4 - In Exercises 9-14, the linear systems are the same...Ch. 3.5 - In Exercises 1-4, each of the linear systems has...Ch. 3.5 - In Exercises 5-8, the linear systems are the same...Ch. 3.5 - Given a quadratic 2++, what condition on and ...Ch. 3.6 - In Exercises 16, find the general solution (in...Ch. 3.6 - In Exercises 16, find the general solution (in...Ch. 3.6 - In Exercises 16, find the general solution (in...Ch. 3.6 - In Exercises 712, find the solution of the given...Ch. 3.6 - In Exercises 712, find the solution of the given...Ch. 3.6 - In Exercises 712, find the solution of the given...Ch. 3.6 - In Exercises 712 , find the solution of the given...Ch. 3.6 - In Exercises 1320, consider harmonic oscillators...Ch. 3.6 - In Exercises 13-20, consider harmonic oscillators...Ch. 3.6 - In Exercises 1320, consider harmonic oscillators...Ch. 3.7 - In Exercises 27 , we consider the one-parameter...Ch. 3.7 - In Exercises 2-7, we consider the one-parameter...
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- For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Month Number (Thousands)Dec 1991 65.60Jan 1992 71.60Feb 1992 78.80Mar 1992 111.60Apr 1992 107.60May 1992 115.20Jun 1992 117.80Jul 1992 106.20Aug 1992 109.90Sep 1992 106.00Oct 1992 111.80Nov 1992 84.50Dec 1992 78.60Jan 1993 70.50Feb 1993 74.60Mar 1993 95.50Apr 1993 117.80May 1993 120.90Jun 1993 128.50Jul 1993 115.30Aug 1993 121.80Sep 1993 118.50Oct 1993 123.30Nov 1993 102.30Dec 1993 98.70Jan 1994 76.20Feb 1994 83.50Mar 1994 134.30Apr 1994 137.60May 1994 148.80Jun 1994 136.40Jul 1994 127.80Aug 1994 139.80Sep 1994 130.10Oct 1994 130.60Nov 1994 113.40Dec 1994 98.50Jan 1995 84.50Feb 1995 81.60Mar 1995 103.80Apr 1995 116.90May 1995 130.50Jun 1995 123.40Jul 1995 129.10Aug 1995…arrow_forwardFor each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Year Month Units1 Nov 42,1611 Dec 44,1862 Jan 42,2272 Feb 45,4222 Mar 54,0752 Apr 50,9262 May 53,5722 Jun 54,9202 Jul 54,4492 Aug 56,0792 Sep 52,1772 Oct 50,0872 Nov 48,5132 Dec 49,2783 Jan 48,1343 Feb 54,8873 Mar 61,0643 Apr 53,3503 May 59,4673 Jun 59,3703 Jul 55,0883 Aug 59,3493 Sep 54,4723 Oct 53,164arrow_forwardConsider the table of values below. x y 2 64 3 48 4 36 5 27 Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.arrow_forward
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