Maximum likelihood estimator of binominal distribution

  1. [tex]
    L(x_1,...,x_n;p)=\Pi_{i=1}^{n}(\stackrel{n}{x_i}) p^{x_i}(1-p)^{n-x_i}
    [/tex]

    Correct so far?

    The solution tells me to skip the [tex]\Pi[/tex]:

    [tex]
    L(x_1,...,x_n;p)=(\stackrel{n}{x}) p^{x}(1-p)^{n-x}
    [/tex]

    This is contradictory to all the examples in my book. Why?
     
    Last edited: May 7, 2009
  2. jcsd
  3. Defennder

    Defennder 2,616
    Homework Helper

    I don't understand why you wrote L(x1...xn,p). I thought the purpose was to estimate p, the probability of a designated success outcome in a Bernoulli trial. So it should be L (p) as p is the only parameter.

    I also don't see any sense in omitting the multiplicative pi symbol. What is x here, anyway? x_i all refer to the observed no. of succeses of each sample size n. So what is x?
     
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