The random variables X and Y are jointly continuous, with a joint PDF of the form

Question

fX,Y(x,y)={cxy,if 0≤x≤y≤1
0,,otherwise,

where c is a normalizing constant.

For x∈[0,0.5], the conditional PDF fX|Y(x|0.5) is of the form ax^b. Find a and b. Your answers should be numbers.

Answer 1

a=8
b=1