If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to _________.

Answer

A

Explanation

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)`