Question

The joint PDF of X and Y is given by fX,Y(x, y) = nx^ne^(?xy) , 0...

The joint PDF of X and Y is given by

fX,Y(x, y) = nx^ne^(?xy) , 0 < x < 1, y > 0,

where n is an integer and n > 2.

(a) Find the marginal PDF of X and its mean.

(b) Find the conditional PDF of Y given X = x.

(c) Deduce the conditional mean and the conditional variance of Y given X = x.

(d) Find the mean and variance of Y .

(e) Find the covariance of X and Y by conditioning on X.

Math   Statistics-And-Probability   
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Answer #1

The given joint pdf is . is an integer and .

a) The marginal pdf of ia

b)

The conditional pdf

c)

d) The marginal pdf of is

We cannot find the mean and variance of Y analytically.

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