Advanced Probability Problems And Solutions Pdf ((install)) <TRUSTED>

E[X2|Y=y]=11−y2⋅(1−y2)3/23=1−y23cap E open bracket cap X squared vertical line cap Y equals y close bracket equals the fraction with numerator 1 and denominator the square root of 1 minus y squared end-root end-fraction center dot the fraction with numerator open paren 1 minus y squared close paren raised to the 3 / 2 power and denominator 3 end-fraction equals the fraction with numerator 1 minus y squared and denominator 3 end-fraction The final conditional expectation is:

So we must integrate over the intersection of $[0, 1]$ and $[z-1, z]$. advanced probability problems and solutions pdf

The Jacobian matrix of this transformation is triangular: 1]$ and $[z-1