Distribution of a quadratic function of a binomial random variable [closed]

Let $X$ be a binomial random variable with parameters $p = 1/2$ and $n = 6$. Find the probability function and the distribution function of $Y = X^2 − 2X$.

-

closed as too localized by cardinal, Benjamin Lim, Did, Ｊ. Ｍ., Zev ChonolesApr 28 '12 at 15:59

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Let $X$ be a probability assignment and $T(X)$ be the time left until it is due. Prove that $T(X) < \varepsilon$. –  cardinal Apr 18 '12 at 3:30
@cardinal That looks like a tautology to me. :P –  user21436 Apr 18 '12 at 3:38
@cardinal: :))) –  Vadim Apr 18 '12 at 3:51

Just Hint: $X$ is a random variable that takes value $k$ from 0 to 6, and $Pr\{X=k\}=\binom{6}{k}\frac{1}{2^6}$.
Now, $Y=X^2-2X$ and can take values $0^2-0=0$,$1^2-2=-1$, $0$, $3$, $8$, $15$ and $24$. Then, $Pr\{Y=0\}=Pr\{X=0 \vee X=2\}$, $Pr\{Y=-1\}=Pr\{X=1\}$ etc.