A binomial discrete random variable, X has a mean of 3 and variance of 2. If X ~ B(n,p), find the values of p and of n.​

Question

A binomial discrete random variable, X has a mean
of 3 and variance of 2. If X ~ B(n,p), find the values
of p and of n.​

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Ngọc Khuê 4 years 2021-07-16T02:44:59+00:00 1 Answers 144 views 0

Answers ( )

  1. Acacia
    0
    2021-07-16T02:46:16+00:00
    Reply

    Since X follows a binomial distribution, its mean and variance are

    np = 3

    np (1 – p) = 2

    Substitute np = 3 in to the second equation to solve for p :

    3 (1 – p) = 2

    1 – p = 2/3

    p = 1/3

    Solve for n :

    n (1/3) = 3

    n = 9

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