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Math Help - bi(n;x,θ)

  1. #1
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    bi(n;x,θ)

    hello
    if x~bi(n;x,θ) then for which θ the probability is the max?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by abdolah View Post
    hello
    if x~bi(n;x,θ) then for which θ the probability is the max?
    Please explain you notation and preferably the exact wording of the problem.

    CB
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  3. #3
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    ok i mean this:
    if we have binomial disribution with parameter x and teta(the probability of each victory) and n then for which teta the binomial probability is the max?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by abdolah View Post
    ok i mean this:
    if we have binomial disribution with parameter x and teta(the probability of each victory) and n then for which teta the binomial probability is the max?
    You have a RV N \sim B(x,\theta)

    Now you ask for what value of \theta is:

    b(n;x,\theta)=\frac{n!}{x!(n-x)!} \theta^n (1-\theta)^{n-1}

    maximised.

    Start by observing the required \theta is a solution of:

    \frac{\partial}{\partial \theta}b(n;x,\theta)=0

    CB
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