What is probability that the two components fail within three months apart ? (the units of x and y are months)
What is probability that the two components fail within three months apart ? (the units of...
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
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
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...
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.
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?
. 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)
4. I. Let Yǐ < ½ < ⅓ < Ya be the order statistics of a random sample of size n = 4 from a distribution with pdf f(x) 322, 0<< 1, zero elsewhere. (a) Find the joint pdf of Ys and Ya (b) Find the conditional pdf of Ys, given Y-y (c) Evaluate Evsl (d) Compute the probability that the smallest of the random sample exceeds the median of the distribution
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
Let X1, X2, ..., Xn represent a
random sample from each of the distributions having the following
pdf. Please find the maximum likelihood estimator for each
case:
(c) f(x; θ)--e-x/e,0 < x < 00, 0 < θ < oo, zero elsewhere (d) f(x; θ) e- , θ x < 00,-00 < θ < 00, zero elsewhere In each case, find the mie of a (x-6)