EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 10, Problem 10.12P
To determine
To find: The value of
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Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) = 10 x over the
interval [10, 10].
In other words, find c E [10, 10] such that f(c)
This function has two values, c₁ and c₂, where c₁ < C₂.
41 =
10
10-11-10) / 10
-10) / f(x)dx.
- 10
-
C2
Using a calculator or computer, sketch the graph of f for k = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe what happens as k changes.
%3D
f(x) has a local minimum. Find the location of the minimum.
X =
Find the y-coordinate of the minimum.
y =
Find the value of k for which this y-coordinate is largest.
k =
How do you know that this value of k maximizes the y-coordinate? Find d² yldk2 to use the second-derivative test.
dy
dk
(Note that the derivative you get is negative for all positive values of k, and confirm that you agree that this means that your value of k
maximizes the y-coordinate of the minimum.)
In the conclusion of the Mean Value Theorem for the function
f(x) = x, [0, 1]
%3D
29 -
Find the value or values of c that satisfy the equation
f(b) - f(a)
b- a
f'(c)
%3D
O A) 5
O B) 9/33
C) 8/27
O D) 6/33
O E) 5/27
Chapter 10 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 10 - The following algorithm will generate a random...Ch. 10 - Prob. 10.2PCh. 10 - Give a technique for simulating a random variable...Ch. 10 - Present a method for simulating a random variable...Ch. 10 - Use the inverse transformation method to present...Ch. 10 - Give a method for simulating a random variable...Ch. 10 - Let F be the distribution functionF(x)=xn0x1 a....Ch. 10 - Prob. 10.8PCh. 10 - Suppose we have a method for simulating random...Ch. 10 - Prob. 10.10P
Ch. 10 - Use the rejection method with g(x)=1,0x1, to...Ch. 10 - Prob. 10.12PCh. 10 - Prob. 10.13PCh. 10 - Prob. 10.14PCh. 10 - Prob. 10.15PCh. 10 - Let X be a random variable on (0, 1) whose density...Ch. 10 - Prob. 10.1STPECh. 10 - Prob. 10.2STPECh. 10 - Prob. 10.3STPECh. 10 - If X is a normal random variable with mean and...Ch. 10 - Prob. 10.5STPE
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