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A device runs until either of two components fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f(x,y)= (x+y)/27 : 0<x<3, 0<y<3 Find Cov(X, Y ).
A device runs until either of two components fails, at which time the device stops running. The joint probability density function of the lifetimes of the two components, both measured in hours, is given by Ш for 0 < z < 3 and 0SyS3, xy(,y)27 0 otherwise. (a) 6 points Find the marginal probability density function for the random variable X. (b) [8 points] Are X and Y independent random variables? Justify your answer. (c) 6 points] Calculate the probability...
b) The joint density of random variables X and Y is f(x,y)=' elsewhere 0' Find cov(X, Y).
2. Two random variables X and Y have joint density function (IN Compute Cov(x,
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...
(1 point) The joint probability density function of X and Y is given by f(x, y) = cx – 16 c”, - <x< 0 < b < co alt 0 < y < 0 Find c and the expected value of X: c = E(X) =
(1 point) If the joint density function of X and Y is f(x, y) = c(22 - y2)e- with OS: < oo and I y I, find each of the following. (a) The conditional probability density of X given Y = y >0. Conditional density fxy(:, y) = (Enter your answer as a function of I, with y as a parameter.) (b) The conditional probability distribution of Y given X = 2. Conditional distribution Fyx (2) = (Enter your answer...
A joint probability density function is given by f(x,y)-c-x(2-x-y), for 0 < x < 1 and 0 < y < 1. Find the value of c to make this a valid density function. A joint probability density function is given by f(x,y)-c-x(2-x-y), for 0
The random variables X and Y have joint density function f(x,y) = x+y, for 0 < x < 1, 0 < y < 1. Find the expected value of W = 3X + Y
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