Question

Suppose that X and Y have the following joint probability function: f(x,y) = { 3x, | 32, if 0 ≤ y ≤1 0, otherwise. a) Find the variance of the random variables X. b) Find the conditional PDF of Y given X.

Answer 1

see below

Explanation:

a) The variance of random variable X is

−

33

4

−

4

33

​

.

b) The conditional PDF of Y given X is:

For

0

≤

�

≤

1

0≤y≤1,

�

(

�

∣

�

)

=

1

f(y∣x)=1.

For

�

y outside the range [0, 1],

�

(

�

∣

�

)

=

0

f(y∣x)=0.