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Math Help - Probability Question

  1. #1
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    Probability Question

    The following was confusing me so any help would be greatly appreciated!

    P(N_i = n_i, i = 1,....,k) = n!/(n_1!n_2!...n_k!) * ((p_1)^(n_1))((p_2)^(n_2))....((p_k)^(n_k)) is known as the multinomial distribution.

    Find the marginal distributions of the multinomial distribution.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by clockingly View Post
    The following was confusing me so any help would be greatly appreciated!

    P(N_i = n_i, i = 1,....,k) = n!/(n_1!n_2!...n_k!) * ((p_1)^(n_1))((p_2)^(n_2))....((p_k)^(n_k)) is known as the multinomial distribution.

    Find the marginal distributions of the multinomial distribution.
    The marginal distribution of N_i is the distribution of N_i ignoring the information about N_j,\ j \ne i, and so is binomial (just by reinterpreting the definition multinomial distribution this should be obvious):

    <br />
P(N_i=n_i) = \frac{n!}{n_i!,(n-n_i)!} p_i^n (1-p_i)^{n-n_i}<br />

    RonL
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