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• ### Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o<

Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o< <p (a) Find E[XY] (b) Find E[X] (c) Find the Covariance of X and Y Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o

• ### Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o< <p (a) Find E[XY]...

Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o< <p (a) Find E[XY] (b) Find E[X] (c) Find the Covariance of X and Y

• ### Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-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...

• ### The joint pdf is given. c(x + y2) for 0 SX S1 and 0 sys1 f(x,y)...

The joint pdf is given. c(x + y2) for 0 SX S1 and 0 sys1 f(x,y) = 0 0.w. Find the conditional pdf of X given Y = y. (a) (b) Fim (r< 10-1)

• ### The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make...

The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...

• ### The joint pdf of X and Y is given by f(x, y) = C,0<x<y<1. a) Determine...

The joint pdf of X and Y is given by f(x, y) = C,0<x<y<1. a) Determine the value of C. b) Determine the marginal distribution of X and compute E(X) and Var(X). c) Determine the marginal distribution of Y and compute E(Y) and Var(Y). d) Compute the correlation coefficient between X and Y.

• ### 3. Suppose the joint PDF of two random variables X and Y are given below 3(xy2...

3. Suppose the joint PDF of two random variables X and Y are given below 3(xy2 + x2y), if o sxs 1,0 Sy s 1, fx.x (x,y) otherwise. (1) What is the covariance of X and Y? (20 points) (2) What is the correlation between X and Y? (20 points) 0,

• ### The joint probability density function (PDF) of random variables X and Y is given by: f(x,y)...

The joint probability density function (PDF) of random variables X and Y is given by: f(x,y) = 4xy for 0 ≤ y ≤ x ≤ 1, and = 0 elsewhere The mean of the random variable X is:

• ### Suppose X, Y are random variables whose joint PDF is given by . 1 0 <...

Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).

• ### How to get the cdf when y>x>0? Thanks 6. The joint probability density function (pdf) of...

How to get the cdf when y>x>0? Thanks 6. The joint probability density function (pdf) of (X, Y) is given by 0y<oo, elsewhere. fxr, y) (a) Find the cumulative distribution function of (X, Y) (b) Evaluate P(Y < X2) (c) Derive the pdf of X and then compute the mean and variance of X (d) Find the pdf of Y and compute the mean and variance of Y (e) Calculate the conditional pdf of Y given X (f) Compute the...