3. For 21, 22 > 0, the beta function is defined as B(21, Z2) := r(1)(2) and can be shown r(21+22) ' to be exactly equal to fx21-1(1 -x)2-'dx. Let X be a continuous random variable with probability density function fx(2 ) = B(a,B) (1 - x)-1, re (0,1 ) 0. otherwise where a, 3 > 0. Compute both E[X'] and var(X)