suppose that x and y are independent random variables taking

suppose that x and y are independent random variables taking values from the positive integers with p(x=k)=2^(-k) and p(y=k)=2*3^(-k). compute p(x<y)

Solution

p(x=k)=2^(-k)

p(y=k)=2*3^(-k)

Let y = r(say)

Then required prob = P(X

= 2^-r(2*3^(-r))

= 2(6)^-r