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A discrete random variable $X$ has the density function $f$ given by $f(-1) = \dfrac 2 {10}, f(0) = c, f(1) = \dfrac 2 {10}, f(2) = \dfrac 1 {10}$.

a) Determine $c$
b) Find the distribution function $F$
c) Show that the random variable $Y=X^2$ has the density function $g$ given by $g(0) = \dfrac 5 {10}, g(1) = \dfrac 4 {10}, g(4) = \dfrac 1 {10}$.

I am having troubles with part C), help would be greatly appreciated! Thanks!

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What seems to be the problem. Since it is discrete, for $(x = 0, y = 0), (x = -1, y =1), (x = 1, y = 1)$ and $(x = 2, y = 4)$. Then it follows $g(0) = f(0), g(1) = f(-1)+f(1)$, and $g(4) = f(2)$. That gives the distribution

$g(0) = 0.5$, $g(1) = 0.4$, $g(4) = 0.1$

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