# 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 $Y = X^2 − 2X$.

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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.