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19. Show that two random variables X and Y cannot possibly have the following properties: EX] = 1, EY] = 3, E[X*|= 5, EY²) = 10, EXY] = 0. %3D %D 20. Let X and Y have the joint PDF f(r.y)-2e , 0

19. Show that two random variables X and Y cannot possibly have the following properties: EX] = 1, EY] = 3, E[X*|= 5, EY²) = 10, EXY] = 0. %3D %D 20. Let X and Y have the joint PDF f(r.y)-2e , 0

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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On the average, anly 30 percent of those accepted for admission will actually es a policy of approving the applications of 450 students. Accepted students make their dec in will attend this college. dependently. Compute the probeability that more than 150 first-year students 14. If X has the PDF f(z)= 1/4,-1<z<3, zero elsewhere, find the PDF of Y =X². 15. Ten hunters are waiting for ducks to fly by. When a flock of ducks flies overhead, the hunters fire at the same time, but each chooses his target at random, independently of the others. If each hunter independently hits his target with probability p, compute the expected number of ducks that escape unhurt when a flock of size 10 flies overhead. 16. Let X1 and X2 be two independent random variables with the same PDF f(z) = exp(-z), r> 0. Find P(X1 < X2). 17. For random variables X1 and X2 defined in problem 16, compute P(X1 < 2X2). 18. Let X be a random variable such that P(X <0) = 0, and let u = E(X) exists. Find an upper bound for P(X 2 2u). 19. Show that two random variables X and Y cannot possibly have the following properties: E[X] = 1, E[Y] = 3, E[X²] = 5, E|Y*] = 10, E[XY] = 0. 20. Let X and Y have the joint PDF f(r.y)-2e", 0<I<y< x. Find EY X-r).
Transcribed Image Text:On the average, anly 30 percent of those accepted for admission will actually es a policy of approving the applications of 450 students. Accepted students make their dec in will attend this college. dependently. Compute the probeability that more than 150 first-year students 14. If X has the PDF f(z)= 1/4,-1<z<3, zero elsewhere, find the PDF of Y =X². 15. Ten hunters are waiting for ducks to fly by. When a flock of ducks flies overhead, the hunters fire at the same time, but each chooses his target at random, independently of the others. If each hunter independently hits his target with probability p, compute the expected number of ducks that escape unhurt when a flock of size 10 flies overhead. 16. Let X1 and X2 be two independent random variables with the same PDF f(z) = exp(-z), r> 0. Find P(X1 < X2). 17. For random variables X1 and X2 defined in problem 16, compute P(X1 < 2X2). 18. Let X be a random variable such that P(X <0) = 0, and let u = E(X) exists. Find an upper bound for P(X 2 2u). 19. Show that two random variables X and Y cannot possibly have the following properties: E[X] = 1, E[Y] = 3, E[X²] = 5, E|Y*] = 10, E[XY] = 0. 20. Let X and Y have the joint PDF f(r.y)-2e", 0<I<y< x. Find EY X-r).
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