Question

X and y are picked at random in aunit circle. Find the joint density of r and x where

Answer 1

Answer:

Step-by-step explanation:

A point (X,Y) is picked at random uniformly in the unit circle.

Find the joint density of R and X, where R2=X2+Y2.

The TA drew a diagram like this and claim that

FR,X(r,t)=r2 when t>r and FR,X(r,t)=0 when t<r

She claimed that it is resulted from the constraints x2+y2≤r2 and x≤t

Hope it helps you....