Asked by JuanPro
Random variables X and Y are distributed according to the joint PDF
fX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise.
1 Find the constant a.
a=
2 Determine the marginal PDF fY(y). (Your answer can be either numerical or algebraic functions of y).
For 0≤y≤1,
fY(y)=
For 1<y≤2,
fY(y)=
3 Determine the conditional expectation of 1/X given that Y=3/2.
E[1/X∣Y=3/2]=
fX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise.
1 Find the constant a.
a=
2 Determine the marginal PDF fY(y). (Your answer can be either numerical or algebraic functions of y).
For 0≤y≤1,
fY(y)=
For 1<y≤2,
fY(y)=
3 Determine the conditional expectation of 1/X given that Y=3/2.
E[1/X∣Y=3/2]=
Answers
Answered by
RVE
1. a= 0.4286
2.
For 0≤y≤1, fY(y)= 0.6429
For 1<y≤2, fY(y)= 0.2142*(4-y^2)
3. E[1/X∣Y=3/2]= 0.5714
2.
For 0≤y≤1, fY(y)= 0.6429
For 1<y≤2, fY(y)= 0.2142*(4-y^2)
3. E[1/X∣Y=3/2]= 0.5714
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