Can I have a detailed, step-by-step explanation on obtaining the answer for the question 6? Thank you very much!

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Can I have a detailed, step-by-step explanation on obtaining the answer for the question 6?

Thank you very much!

 

 

 

5.
S(91 + 2y2) ;0 < y1 < 1
; otherwise
fyY2(Y1, Y2) =
Find the following.
(i) E (Y1|Y2 = )
(ii) V (Y1|Y2 = })
6. Let Y1 and Y, have a joint density function given by,
[ 3y1 ;0< y2 < yı <1
fr,Y,(y1, Y2) =
;otherwise
Find
(i) Find the marginal density function of Y1, Y2
(ii) Are Y1 and Y2 independent ?
(iii) Find E(Y1Y2).
(iv) Find E(Y1) and E(Y2).
(v) Find Cov(Y1,Y2).
(vi) Find V (Y1) and V(Y2)
(vii) Find the conditional density function of Y2 given Y1 = Y1
(viii) Find E(Y2|Y1 = y1).
Transcribed Image Text:5. S(91 + 2y2) ;0 < y1 < 1 ; otherwise fyY2(Y1, Y2) = Find the following. (i) E (Y1|Y2 = ) (ii) V (Y1|Y2 = }) 6. Let Y1 and Y, have a joint density function given by, [ 3y1 ;0< y2 < yı <1 fr,Y,(y1, Y2) = ;otherwise Find (i) Find the marginal density function of Y1, Y2 (ii) Are Y1 and Y2 independent ? (iii) Find E(Y1Y2). (iv) Find E(Y1) and E(Y2). (v) Find Cov(Y1,Y2). (vi) Find V (Y1) and V(Y2) (vii) Find the conditional density function of Y2 given Y1 = Y1 (viii) Find E(Y2|Y1 = y1).
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