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This question is kind of a follow up of another question I had: Asymptotic normal distribution via the central limit theorem

There I had to calculate the estimator for $p$ (meaning $p$ for success) and approximate it's distribution by approximation with a normal distribution.

Now I would like to get the exact distribution of $p$.

I got already the following hint: "You have the functional form of $\hat{p}$. Look up how we derive the distribution of a function of a discrete random variable." Unfortunately that did not lead me to a solution...

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Michael
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    You know that $\hat{p}=X/n$ where $X\sim Bin(n,p)$. So you know the distribution of $X$. What does that tell you about the distribution of $X/n$? – MånsT Oct 28 '13 at 08:15
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    If you had a binomial variable, $X\sim \text{bin}(n,p)$, could your write its probability function, $\text{P}(X=x)$? Now let $Y = 2X$. Can you write the p.f. for $Y$? Now let $Z = cX$; can you write the p.f. for $Z$? What if $c=\frac{1}{n}$? – Glen_b Oct 28 '13 at 23:35

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