Let Y 1 and Y 2 be defined by the following joint PDF f ( y...

Question

Question

Let Y 1 and Y 2 be defined by the following joint PDF f ( y 1 , y 2 ) = ( 6(1 − y 2 ) 0 < y 1 < y 2 < 1, 0 otherwise

(a) (2 pts) Prove that f ( y 1 , y 2 ) is a valid density function.

(b) (2 pts) Find the marginal PDF of Y 2 .

(c) (2 pts) Use the marginal PDF of Y 2 to find E ( Y 2 ).

(d) (2 pts) Find the conditional PDF of Y 1 | Y 2 = y 2 .

(e) (2 pts) Find E ( Y 1 | Y 2 ) and Var ( Y 1 | Y 2 ), using the named distribution in (d).

(f) (2 pts) Find E ( Y 1 ) and Var ( Y 1 )using the Adam’s and Eve’s laws, respectively.

Answer 1

Answer #1

this is the problem of joint distribution function

Answer 2

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