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Math Help - [SOLVED] Need help with integration

  1. #1
    Sivaram
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    [SOLVED] Need help with integration

    Hi,

    I am trying to integrate the following

    Integral of x*n!/x!(n-x)! *p^(x)*(1-p)^(n-x)dx limits being (x=0,n)

    I applied the rule of integration by parts as follows -

    Let u = x & dv = n!/x!(n-x)!*p^(x)*(1-p)^(n-x)dx

    Therefore, du=dx
    V= integral n!/x!(n-x!)*p^(x)*(1-p)^(n-x)dx

    I am unable to proceed beyond this point. Can somebody help me here? What would be the final solution for this if we apply limits (0,n)?

    Thanks,
    Sivaram.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Sivaram View Post
    Hi,

    I am trying to integrate the following

    Integral of x*n!/x!(n-x)! *p^(x)*(1-p)^(n-x)dx limits being (x=0,n)

    I applied the rule of integration by parts as follows -

    Let u = x & dv = n!/x!(n-x)!*p^(x)*(1-p)^(n-x)dx

    Therefore, du=dx
    V= integral n!/x!(n-x!)*p^(x)*(1-p)^(n-x)dx

    I am unable to proceed beyond this point. Can somebody help me here? What would be the final solution for this if we apply limits (0,n)?

    Thanks,
    Sivaram.
    First try replacing the factorials with appropriate gamma functions (factorial
    is only defined for non-negative integers, you need something defined for all
    reals in (0,n). Alternatively replace the integral with a summation from 0 to
    n, which is 1 as you are summing the binomial distribution with parameters
    n, p over all possible outcomes.

    If the latter is the case, your original sum would heve been the mean of the
    binomial distribution with probability of success on a single trial of p, and
    a total of n trials, this is n*p.

    RonL

    RonL
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