A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 10, Problem 10.2P
To determine
To calculate: technique for simulating random variable using density
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8. The density function for the random variable X is f(x). Find E(3X - 1).
) = √(= (2x + 1
(2x + 1)
E(3X - 1) =
f(x) =
1 < x < 2
0 elsewhere
The density function of two random variables X and Y is
fxy (x, y) = 16 e-4 (x+y). u (x) u (y)
Find the mean of the function
(X, ¥)= 5 for 0 < X s;
1
= -1 for < X and lor< Y
2
= 0 for all other X and Y
For two random variables X and Y, the joint density function is
Find (a) the correlation
fxy(x, y) = 0.158(x+1) 8(y)+0.18(x) 8(y)+0.18(x)(y-2)
8(x-1)8(y+2)+0.28(x-1)(y-1)+0.05(x-1)(y-3)
+0.4
Chapter 10 Solutions
A First Course in Probability
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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