Let X1 and X2 be a random sample of size 2 from a distribution with probability density function f(x) = exp(-x) , 0 <x < infinity. and f(x)= 0 elsewhere.
Now, let Y1= X1+ X2.
Y2 = X1/(X1+X2).
Prove that Y2 and Y2 are independent.
Let X1 and X2 be a random sample of size 2 from a distribution with probability density function f(x) = exp(-x) , 0 <x < infinity. and f(x)= 0 elsewhere.
Now, let Y1= X1+ X2.
Y2 = X1/(X1+X2).
Prove that Y2 and Y2 are independent.