Maximum likelihood estimator of binominal distribution

[superwolf]

<br /> L(x_1,...,x_n;p)=\Pi_{i=1}^{n}(\stackrel{n}{x_i}) p^{x_i}(1-p)^{n-x_i}<br />

Correct so far?

The solution tells me to skip the \Pi:

<br /> L(x_1,...,x_n;p)=(\stackrel{n}{x}) p^{x}(1-p)^{n-x}<br />

This is contradictory to all the examples in my book. Why?

 

[Defennder]

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?