Let $X ∼ E(2)$. Find the density function $f_Y$ of $Y = X^3$.
Anyway I could get help starting out on this problem? I'm stumped as to how to approach this.
Let $X ∼ E(2)$. Find the density function $f_Y$ of $Y = X^3$.
Anyway I could get help starting out on this problem? I'm stumped as to how to approach this.
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Since $Y = X^3$ is one to one over the possible values of $X$, then we can apply the one to one transformation; $dy/dx = 3x^2$, $x = \sqrt[3]y$, and $$f_Y(y) = \frac{f_X(\sqrt[3]y)}{|dy/dx|_{\sqrt[3]y}}$$.
You could also compute the cdf by doing $$P(Y \leq y) = P(X^3\leq y) = P(X\leq \sqrt[3]y).$$