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statistic

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The random variable x represents the number of boys in a family with three children.
Assuming that births of boys and girls are equally likely, find the mean and standard
deviation for the random variable x.

  • statistic - ,

    This is a binomial distribution with parameters
    n=3 (number of trials in the experiment)
    p=1/2 (probability of boys, X)
    q=1-p (probability of girls)

    For a random variable X with a binomial distribution (n,p,q), then
    E(x)=μ=np
    σ²=npq
    where σ=standard deviation (of population)

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