If x is a random variable with p.m.f. as follows. aligned & P(X=x)= 5 16 , x=0,1 & = k x 48 , x=2, then E(x)= & = 1 4 , x=3 aligned

Step-by-step solution

From given data, we write When x =0, P = 5 16 = 15 48 aligned & x=1, P= 5 16 = 15 48 & x=2, P= 2 k 48 & x=3, P= 1 4 = 12 48 aligned Here Pi =1 aligned & 15 48 + 15 48 + 2 k 48 + 12 48 =1 k =3 & When x =2, P = 6 48 = 1 8 aligned aligned & Now E = p _ i x _ i & = [ ( 5 16 )(0) ]+ [ ( 5 16 )(1) ]+ [ ( 1 8 )(2) ]+ [ ( 1 4 )(3) ]=0+ 5 16 + 1 4 + 3 4 = 21 16 =1.3125 aligned