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Graph the distribution function $F(x)=1-e^{-3 x}$ if $x > 0, F(x)=0$ if $x \leq 0,$ and the density $f(x)$. Find $x$ such that $F(x)=0.9$...

Question

Graph the distribution function $F(x)=1-e^{-3 x}$ if $x > 0, F(x)=0$ if $x \leq 0,$ and the density $f(x)$. Find $x$ such that $F(x)=0.9$

Graph the distribution function $F(x)=1-e^{-3 x}$ if $x > 0, F(x)=0$ if $x \leq 0,$ and the density $f(x)$. Find $x$ such that $F(x)=0.9$



Answers

Let $ f(x) = 30x^2 (1 - x)^2 $ for $ 0 \le x \le 1 $ and $ f(x) = 0 $ for all other values of $ x $.
(a) Verify that $ f $ is a probability density function.
(b) Find $ P(X \le \frac{1}{3}) $.


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