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math

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let the random variable x denote the number of girls in a five-child family. if the probability of a female birth is .5

find the probability of 0,1,2,3,4, and 5 girls in a five-child family.
construct the binomial distribution and draw the histogram associated with the experiment
compute the mean and the standard deviation of the random variable x

  • math - ,

    for binomial coefficients use
    C(n,k) = n!/(k![n-k]!)
    here n = 5 and k is zero through five
    or just use Pascal triangle
    for n = 5
    they are:
    1 5 10 10 5 1
    then
    P(k girls) = C(n,k) p^k p^(5-k)
    so for example
    p(4 girls )= 5 (.5)^4 (.5)^1
    = 5 (.5)^5 = .15625

    The mean of a binomial distribution = n p so here = 5(.5) = 2.5
    The sigma^2 = n p (1-p)
    so here sigma^2 = 5(.5)(.5) = 5/4
    so sigma = (1/2) sqrt 5 = 1.12

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