Probability Distribution Function? An urn contains 8 green balls and 17 yellow balls. A ball is drawn from the urn and its color is noted and then the ball is placed back in the urn. 5 balls are drawn this way.
Let $X$ denote the yellow balls drawn. Find the probability distribution function of $X$.
PDF: $X\sim\mathrm{Bin}(n,p)$
$X\sim \mathrm{Bin}(5,\frac{17}{25})$
$p(x) = \binom{n}{k}p^k(1-p)^{n-k}$
$p(x) = \binom{5}{k}\left(\frac{17}{25}\right)^k(1-\frac{17}{25})^{5-k}$
I'm wondering if what I did so far was correct and if so, what would $k$ be?
EDIT: fixed value for p
 A: You've written both $x$ and $k$, but they're both the same thing.  You should pick just one letter --- either $x$ or $k$ or something else --- and use it throughout. Also, you have the wrong numerator in $1/25$.
Also, notice that I changed $\frac 1 {25}^k$ to $\left(\frac 1 {25}\right)^k$.  The former looks as if it's $\dfrac{1^k}{25}$, which is wrong.
A: Your steps were mostly correct.  The value of the parameter $p$ should be $17/25$, and the argument $x$ for the probability mass function $p()$ should have been used in its expression where you used $k$ 
(You might also want to use a slightly different symbol for the pmf and the parameter to avoid confusion.)
$$X\sim {\cal Bin}(n, p) \iff p_{\small X}(k) =\begin{cases} \dbinom{n}{k}p^k\,(1-p)^{(n-k)} &: k\in\{0,.,n\}\\ 0&:\text{elsewhere}\end{cases}$$
So for $n=5$, $p=17/25$ therefore:
$$X\sim {\cal Bin}(5, 17/25) \iff p_{\small X}(k) =\begin{cases} \dbinom{5}{k}\dfrac{17^k\,8^{(5-k)}}{25^5}&: k\in\{0,1,2,3,4,5\}\\ 0&:\text{elsewhere}\end{cases}$$
