The probability function of a random variable X is given by P(X=k)=c k^2 , where c is a constant and k 0,1,2,3,4 . If ^2 is the variance of X and is the mean of X , then ^2+ ^2=

Step-by-step solution

Given probability function P(X=k)=C k^2 , where C is a constant and K 0,1,2,3,4 array ll & ^2=E (x^2 )- ^2 & ^2+ ^2=E (x^2 )= (x_i^2 ) P (x_i ) = & 0 (C(0)^2 )+1 (C(1)^2 )+4 (C(2)^2 )+9 (C (3^2 ) )+16 (C(4)^2 ) = & C+16 C+81 C+256 C array array ll & P (x_i )=1 C+4 C+9 C+16 C=1 & 30 C=1 C= 1 30 array Put the value of C , in Eq. (i), we get So, ^2+ ^2= 354 30 =11.8 . Hence, option (b) is correct.