Let a random variable X take values 0,1,2,3 with P ( X =0)= P ( X =1)= p , P ( X =2)= P ( X =3) and E ( X ^2 )=2 E ( X ) . Then the value of 8 p -1 is :

Step-by-step solution

aligned & 2 p+2 q= 1 2 & p+q & E (x^2 )= _ i=0 ^3 x_i^2 p (x_i )=0 p+1 p+4 q+9 q & =p+13 q & E(x)= _ i=0 ^3 x_i^2 p (x_i )=0 p+1 p+2 q+3 q=p+5 q & p+13 q=2(p+5 q) & p=3 q & So, q= 1 8 & p= 3 8 & So, 8 p-1=2 Option (2) aligned