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Question:

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

34

116

916

1516

Solution:

For binomial distribution,Mean=np=2(1)Variance=npq=1⇒2q=1⇒q=12⇒p=12(∵p+q=1)⇒n=4

P(X≥1)=1-P(X=0)=1-⁴C₀(1/2)⁴(1/2)⁰=1-(1/16)=15/16