Fundamentals Of Differential Equations And Boundary Value Problems Plus Mylab Math With Pearson Etext -- Title-specific Access Card Package (7th ... Fundamentals Of Differential Equations)
7th Edition
ISBN: 9780134768717
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Publisher: PEARSON
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Chapter 11.8, Problem 13E
To determine
To prove:
The substitution
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5) State any theorems that you use in determining your solution.
a) Suppose you are given a model with two explanatory variables such that:
Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n
Using partial differentiation derive expressions for the intercept and slope
coefficients for the model above.
[25 marks]
b)
A production function is specified as:
Yi = α + B₁x1i + ẞ2x2i + Ui,
i = 1, 2, ... n,
u₁~N(0,σ²)
where:
y = log(output), x₁ = log(labor input), x2 = log(capital input)
The results are as follows:
x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10,
= 8, Syy = 10,
S2y
n = 23 (individual firms)
i) Compute values for the intercept, the slope coefficients and σ².
[20 marks]
ii)
Show that SE (B₁) = 0.102.
[15 marks]
iii)
Test the hypotheses: ẞ1
=
1 and B2 = 0, separately at the 5%
significance level. You may take without calculation that SE (a) = 0.78
and SE (B2) = 0.102
[20 marks]
iv)
Find a 95% confidence interval for the estimate ẞ2.
[20 marks]
Page < 2
of 2
- ZOOM +
The set of all 3 x 3 upper triangular matrices
6) Determine whether each of the following sets, together with the standard
operations, is a vector space. If it is, then simply write 'Vector space'. You do not
have to prove all ten vector space axioms. If it is not, then identify one of the ten
vector space axioms with its number in the attached sheet that fails and also show
that how it fails.
a) The set of all polynomials of degree four or less.
b) The set of all 2 x 2 singular matrices.
c) The set {(x, y) : x ≥ 0, y is a real number}.
d) C[0,1], the set of all continuous functions defined on the interval [0,1].
7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and
show that it is orthogonal to both u and v.
8) a) Find the equation of the least squares regression line for the data points
below.
(-2,0), (0,2), (2,2)
b) Graph the points and the line that you found from a) on the same Cartesian
coordinate plane.
1. A consumer group claims that the mean annual consumption of cheddar cheese by a person in
the United States is at most 10.3 pounds. A random sample of 100 people in the United States has
a mean annual cheddar cheese consumption of 9.9 pounds. Assume the population standard
deviation is 2.1 pounds. At a = 0.05, can you reject the claim? (Adapted from U.S. Department of
Agriculture)
State the hypotheses:
Calculate the test statistic:
Calculate the P-value:
Conclusion (reject or fail to reject Ho):
2. The CEO of a manufacturing facility claims that the mean workday of the company's assembly
line employees is less than 8.5 hours. A random sample of 25 of the company's assembly line
employees has a mean workday of 8.2 hours. Assume the population standard deviation is 0.5
hour and the population is normally distributed. At a = 0.01, test the CEO's claim.
State the hypotheses:
Calculate the test statistic:
Calculate the P-value:
Conclusion (reject or fail to reject Ho):
Statistics
Chapter 11 Solutions
Fundamentals Of Differential Equations And Boundary Value Problems Plus Mylab Math With Pearson Etext -- Title-specific Access Card Package (7th ... Fundamentals Of Differential Equations)
Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 3ECh. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 7ECh. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 9ECh. 11.2 - In Problems 1-12, determine the solutions, if any,...
Ch. 11.2 - Prob. 11ECh. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 13ECh. 11.2 - In Problems 13-20, find all the real eigenvalues...Ch. 11.2 - In Problems 13-20, find all the real eigenvalues...Ch. 11.2 - Prob. 16ECh. 11.2 - In Problems 13-20, find all the real eigenvalues...Ch. 11.2 - In Problems 13-20, find all the real eigenvalues...Ch. 11.2 - In Problems 13-20, find all the real eigenvalues...Ch. 11.2 - In Problems 13-20, find all the real eigenvalues...Ch. 11.2 - In Problems 23-26, find all the real values of ...Ch. 11.2 - In Problems 23-26, find all the real values of ...Ch. 11.2 - In Problems 23-26, find all the real values of ...Ch. 11.2 - In Problems 23-26, find all the real values of ...Ch. 11.3 - In Problem 1-6, convert the given equation into...Ch. 11.3 - In Problem 1-6, convert the given equation into...Ch. 11.3 - Prob. 3ECh. 11.3 - In Problem 1-6, convert the given equation into...Ch. 11.3 - Prob. 5ECh. 11.3 - In Problems 1-6, convert the given equation into...Ch. 11.3 - Prob. 7ECh. 11.3 - In problem 7-11, determine whether the given...Ch. 11.3 - In problem 7-11, determine whether the given...Ch. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Let be an eigenvalue and a corresponding...Ch. 11.3 - Prob. 15ECh. 11.3 - Show that if =u+iv is an eigenfunction...Ch. 11.3 - In Problems 17 -24, a determine the normalized...Ch. 11.3 - In Problems 17 -24, a determine the normalized...Ch. 11.3 - In Problems 17 -24, a determine the normalized...Ch. 11.3 - In Problems 17 -24, a determine the normalized...Ch. 11.3 - In Problems 17 -24, a determine the normalized...Ch. 11.3 - In Problems 17 -24, a determine the normalized...Ch. 11.3 - Prob. 25ECh. 11.3 - Prove that the linear differential operator...Ch. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - In Problems 7-10, find theadjointoperator and its...Ch. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - In Problems 7-10, find the adjoint operator and...Ch. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.5 - Prob. 1ECh. 11.5 - In Problems 1-8, find a formal eigenfunction...Ch. 11.5 - Prob. 3ECh. 11.5 - In Problems 1-8, find a formal eigenfunction...Ch. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - In Problem 9-14, find a formal eigenfunction...Ch. 11.5 - In Problem 9-14, find a formal eigenfunction...Ch. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - In Problem 9-14, find a formal eigenfunction...Ch. 11.5 - Derive the solution to Problem 12 given in...Ch. 11.6 - Prob. 1ECh. 11.6 - Prob. 2ECh. 11.6 - Prob. 3ECh. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - In Problems 1-10, find the Greens function G(x,s)...Ch. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - In problems 11 -20, use Greens functions to solve...Ch. 11.6 - In problems 11 -20, use Greens functions to solve...Ch. 11.6 - In Problems 11-20, use Greens functions to solve...Ch. 11.6 - In Problems 11-20, use Greens functions to solve...Ch. 11.6 - In Problems 11-20, use Greens functions to solve...Ch. 11.6 - In Problems 11-20, use Greens functions to solve...Ch. 11.6 - In Problems 11-20, use Greens functions to solve...Ch. 11.6 - Derive a formula using a Greens function for the...Ch. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Prob. 25ECh. 11.6 - Prob. 26ECh. 11.6 - Prob. 31ECh. 11.7 - Prob. 2ECh. 11.7 - Prob. 3ECh. 11.7 - Prob. 4ECh. 11.7 - Prob. 5ECh. 11.7 - Prob. 6ECh. 11.7 - Prob. 8ECh. 11.7 - Prob. 9ECh. 11.7 - Prob. 10ECh. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - Show that the only eigenfunctions of 23-24...Ch. 11.7 - a. Use formula 25 to show that Pn(x) is an odd...Ch. 11.7 - Prob. 16ECh. 11.8 - Prob. 1ECh. 11.8 - Prob. 2ECh. 11.8 - Prob. 3ECh. 11.8 - Can the function (x)=x4sin(1/x) be a solution on...Ch. 11.8 - Prob. 6ECh. 11.8 - Prob. 7ECh. 11.8 - Prob. 8ECh. 11.8 - Prob. 9ECh. 11.8 - Prob. 10ECh. 11.8 - Prob. 11ECh. 11.8 - In equation (10), assume Q(x)m2 on [a,b]. Prove...Ch. 11.8 - Prob. 13ECh. 11.8 - Show that if Q(x)m20 on [a,), then every solution...Ch. 11.RP - Find all the real eigen-values and eigen-functions...Ch. 11.RP - Prob. 2RPCh. 11.RP - a. Determine the eigenfunctions, which are...Ch. 11.RP - Prob. 4RPCh. 11.RP - Use the Fredholm alternative to determine...Ch. 11.RP - Find the formal eigenfunction expansion for the...Ch. 11.RP - Find the Greens function G(x,s) and use it to...Ch. 11.RP - Find a formal eigenfunction expansion for the...Ch. 11.RP - Let (x) be a nontrivial solution to...Ch. 11.RP - Use Corollary 5 in Section 11.8 to estimate the...
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