Question

If the mean and the variance of a binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to: Select the correct answer from above options

Answer 1

Correct Answer - A For Biomial distribution, mean =np and variance=npq `:. " "np=2 " "and " "npq=1" "` [given] `rArr " "q=1//2 " and "p+q=1` `rArr " "p=1//2` `:. " "n=4,p=q=1//2` Now, `P(X gt1)=1-{P(X=0)+P(X=1)}` `=1-overset(4)C_(0)((1)/(2))^(0)((1)/(4))^(4)-overset(4)""C_(1)((1)/(2))^(1)((1)/(2))^(3)` `=1=-(1)/(16)-(4)/(16)=(11)/(16)`