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Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X Problem 4: Two components of a minicomputer have the following...
Problem 4: Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: xe-(+) ;x>0;y>0 0 ; elsewhere fx y(x,y)- (a) Explain whether the lifetimes of two components are independent based on probability. (b) Compute the probability that the lifetime (X) exceeds 3.5 (c) Compute the probability that the lifetime of at least one component exceeds 3.5. (d) Compute the marginal pdf of X Problem 4: Two components of a minicomputer have the following...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: f (x, y) 5 5xe2x(11y) x $ 0 and y $ 0 0 otherwise a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf’s of X and Y? Are the two lifetimes independent? Explain. c. What is the probability that the lifetime of at least one component exceeds 3? 12. Two components...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: FY 1 xe A1 + + x2 0 and v2 0 1 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe X(1+y)dy = e X for x 2 0 dx = 1 (1 + vi for y xe X(1+y)dx...
Two components of a minicomputer have the following joint pdf for their useful lifetimesX and Y (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? x(1+y)dx = e-x for x 0 ye (1x)dy e for y 2 0 ye x(1+y)dx= for x 0 xe-x(1+y)dy-e* for x 2 0 for y e 0 What is the marginal pdf of Y?...
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
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
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. -30 a) The joint pdf of random variables X and Y is given by f(x,y) = 27ye-3 y<x<0, y >0. Show that the joint moment generating function(mgf) of X and Y is 27 M(t1, tz) = tı <3, tı + t, <3 (3 - tı) (3 - 7ı - t2) Use the joint mgf to obtain Cov(X,Y). b) Let X1, X2, X3 be independent random variables representing the lifetime of 3 electronic components with the following pdf, where X...
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.