If the p.m.f. of a r.v. X is given by P ( X =x)= ( array l 5 x array ) 2⁵ if x=0,1,2, 5=0 otherwise then which of the following is not true?

Step-by-step solution

(B) aligned P(X 2) &=P(X=0)+P(X=1)+P(X=2) &= 5 0 2⁵ + 5 1 2⁵ + 5 2 2⁵ = 1+5+10 2⁵ = 16 2⁵ P(X 4) &=P(X=4)+P(X=5) &= C₄ 2⁴ + C₆ 2⁶ = 5+1 2⁵ = 6 2⁵ aligned aligned P ( X 3) &= P ( X =0)+ P ( X =1)+ P ( X =2)+ P ( X =3) &= ⁵ C ₀ 2⁵ + ⁵ C ₁ 2⁵ + ⁵ C ₂ 2⁵ + ⁵ C ₃ 2⁵ = 1+5+10+10 2⁵ = 26 2⁵ P ( X 3) &= P ( X =3)+ P ( X =4)+ P ( X =5) &= ⁵ C ₃ 2⁵ + ⁵ C ₄ 2⁵ + ⁵ C ₅ 2⁵ = 10+5+1 2⁵ = 16 2⁵ P ( X 1) &= P ( X =0)+ P ( X =1) &= ⁵ C ₀ 2⁵ + ⁵ C ₁ 2⁵ = 1+5 2⁵ = 6 2⁵ aligned