The p.m.f. of a random variable X is given by aligned P [ X =x] & = 5 x 2^5 , if x=0,1,2,3,4,5 & =0, otherwise aligned Then which of the following is not correct?

Step-by-step solution

aligned P ( X 1) & = P ( X =0)+ P ( X =1) & = ^5 C ₀ 2^5 + ^5 C ₁ 2^5 = 6 2^5 P ( X 2) & = P ( X =0)+ P ( X =1)+ P ( X =2) & = ^5 C ₀ 2^5 + ^5 C ₁ 2^5 + ^5 C ₂ 2^5 = 16 2^5 aligned aligned P ( X 3) & = P ( X =3)+ P ( X =4)+ P ( X =5) & = ^5 C ₃ 2^5 + ^5 C ₄ 2^5 + ^5 C ₅ 2^5 = 16 2^5 P ( X 3) & = P ( X =0)+ P ( X =1)+ P ( X =2) & + P ( X =3) & = ^5 C ₀ 2^5 + ^5 C ₁ 2^5 + ^5 C ₂ 2^5 + ^5 C ₃ 2^5 = 26 2^5 P ( X 4) & = P ( X =4)+ P ( X =5) & = ^5 C ₄ 2^5 + ^5 C ₅ 2^5 = 6 2^5 aligned P ( X 2) P ( X 3) is not true.