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2) Let X and Y be independent exponential random variables with means E[X] = 0 and...
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
Let X, Y be random variables with f(x, y) = 1,-y < x < y, 0 < y < 1. Show that Cov(X,Y) = 0. Are X, Y independent?
Suppose X and Y are independent random variables with Exponential(2) distribution (Section 6.3). We say X ~ Exponential(2) if its pdf is f(x) = -1/2 for x > 0.
Suppose that the standard normal random variables X and Y are independent. Find P(0 < X<Y). 8 O 1 4T 0 1 8л Ala
PROB 4 Let Xi and X2 be independent exponential random variables each having parameter 1 i.e. fx(x) = le-21, x > 0, (i = 1,2). Let Y1 = X1 + X2 and Y2 = ex. Find the joint p.d.f of Yi and Y2.
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) = 2. o if 0<x< 1 else Find EY] where Y = min{X1, X2, X3, X4}.
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
Let f(x,y) = 12e-2(x+y), x > 0, y > 0. Show that X, Y are independent. What are the marginal PDFs of each?
please explain each step 5.21 Let X and Y be independent random variables with fae-ax, x>0 fx(x) = 10. otherwise and Be-Bt, x>0 fr(y) = 10 otherwise where a and B are assumed to be positive constants. Find the PDF of X + Y and treat the special case a = B separately.
Let X and Y be random variables with joint density function f(x,y) бу 0 0 < y < x < 1 otherwise The marginal density of Y is fy(y) = 3y (1 – y), for 0 < y < 1. True False