What is the probability the component with life time X would fail 3 months before the other one?
What is the probability the component with life time X would fail 3 months before the...
What is probability that the two components fail within three months apart ? (the units of x and y are months) ine have the followin pdf f(x,y) = (50-z-y) for 0 < z < 50-y < 50 and zero 125,000 elsewhere
Compute the covariance of X, Y Compute the expected life of the machine ine have the followin pdf f(x,y) = (50-z-y) for 0 < z < 50-y < 50 and zero 125,000 elsewhere
2. Suppose X and Y have the joint pdf fxy(x, y) = e-(x+y), 0 < x < 00, 0 < y < 0o, zero elsewhere. (a) Find the pdf of Z = X+Y. (b) Find the moment generating function of Z.
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x y) for 0<50-y < 50 and zero elsewhere a. What is the probability that both components are functioning 20 months from now. b. What is the probability the component with life time X would fail 3 months before the other one? c. Compute the covariance of X, Y d. Compute the expected life of the machine e. What is probability that the two components...
22 If f(L,y) = 561, for 0 <<<y<1. find o elsewhere, (a) f(y) (b) f(z|y) (c) E[X | Y = y) (d) EX | Y = 0.5]
Let X1, ..., Xn be a random sample from a population with pdf f(x 1/8,0 < x < θ, zero elsewhere. Let Yi < < Y, be the order statistics. Show that Y/Yn and Yn are independent random variables
2. Let f(x,y) = e-r-u, 0 < x < oo, 0 < y < oo, zero elsewhere, be the pdf of X and Y. Then if Z = X + Y, compute (a) P(Z 0). (b) P(Z 6) (c) P(Z 2) (d) What is the pdf of Z?
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X
Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
Problem 3: X and Y are jointly continuous with joint pdf 0<x<2, 0<y<x+1 f(x,y) = 17 0, Elsewhere a) Find P(X < 1, Y < 2). b) Find marginal pdf's of X. c) f(x|y=1). d) Find E(XY). dulrahim