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attend this college. 14. If X has the PDF f(x) = 1/4,-1

attend this college. 14. If X has the PDF f(x) = 1/4,-1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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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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