(a)
The marginal pdf of Y is
(b)
The conditional pdf of X given Y=y is
(c)
The expected value is
(d)
22 If f(L,y) = 561, for 0 <<<y<1. find o elsewhere, (a) f(y) (b) f(z|y) (c)...
Let f(x, y) = kxy, for 0 <x< 1 and 0 <y<1 and 0 elsewhere, a) Find k b) Find marginal pdfs. c) Are X and Y independent? d) Find P(X<0.5, Y>0.5).
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0 (a) What is c? Plot the pdf (b) Plot the edf of X. (c) Find P(X 0.5<0.3).
For f(x, y) = k(x2 + y2), 0<x< 1 and 0 <y<1 and 0 elsewhere: a) Find k. b) Are X and Y independent? c) Find P(X<0.5, Y>0.5), P( X = 0.5, Y>0.5).
⑤. (a) Find cov(W,Z) for W and Z defined in Problem 1. e loint densitv of random variables 3r, if 0 <yKrK, (, elsewhere. Find cov(X, Y).
What is the probability the component with life time X would fail 3 months before the other one? ine have the followin pdf f(x,y) = (50-z-y) for 0 < z < 50-y < 50 and zero 125,000 elsewhere
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0 < z < i, zero elsewhere, be the pdf of X. (a) Compute E(1/X). (b) Find the edf and the pdf of Y 1/X c) Compute E(Y) and compare this result with the answer obtained in Part (a).
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
6. Let f(x,y) = 1 if 0 < y < 2x, 0<x<1, and 0 otherwise. Find the following: a) f(y|x) b) E(Y|X = x) c) The correlation coefficient, p, between X and Y
Let X, Y E [0, 1] be distributed according to the joint distribution Íxy (z, y) 6xy2 . Let -XY-3 . Find P(Z < 1 /2)