If the mean and variance of a binomial variate X are 8 and 4 respectively, then P(X < 3) equals to

Step-by-step solution

Given, mean of binomial variable, n p=8 and variance of binomial variable, n p q=4 q= 1 2 and aligned p & =1-q & =1- 1 2 = 1 2 aligned and n ( 1 2 )=8 n=16 aligned & P(X < 3)=P(X=0)+P(X=1)+P(X=2) & = ¹⁶ C₀ ( 1 2 )^0 ( 1 2 )¹⁶⁻⁰+ ¹⁶ C₁ ( 1 2 )^1 ( 1 2 )¹⁶⁻¹ & + ¹⁶ C₂ ( 1 2 )^2 ( 1 2 )¹⁶⁻² & =1 ( 1 2 )¹⁶+16 ( 1 2 )¹⁶+120 ( 1 2 )¹⁶= 137 2¹⁶ & aligned