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The mean and variance of a random variable X having a binomial distribution are `4 and 2` respectively. The `P(X=1)` is

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The mean and variance of a random variable X having a binomial distribution are `4 and 2` respectively. The `P(X=1)` is A. `1//4` B. `1//32` C. `1//16` D. `1//8` Select the correct answer from above options

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Correct Answer - B Let n and p be the parameters of the binomial distribution. We have, Mean `=4` and Variance `=2` `rArr np=4 and npq=2` `rArr p=1//2 =q and n=8` `therefore` Required Probability `=P(X-1)=.^8C_(1)((1)/(2))^1((1)/(2))^7=(1)/(32)`

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