I think there is some mistake in the question..As X belongs to binomial distribution and Y belongs to uniform distribution in range [0,1] ,we should have both X and Y as non negative numbers..

Also the values that X can take is : 0 to 5 as value of n in binomial distribution B(5,1/2) = 5 and hence X cannot exceed 5..

Also X+Y <= 2 and X + Y >= 5 cannot hold simultaneously as X and Y are non negative numbers..

Hence the question should be wrong somewhere..

Also the values that X can take is : 0 to 5 as value of n in binomial distribution B(5,1/2) = 5 and hence X cannot exceed 5..

Also X+Y <= 2 and X + Y >= 5 cannot hold simultaneously as X and Y are non negative numbers..

Hence the question should be wrong somewhere..