(See) Suppose that X is a continuous random variable with probability density of the form f(x)= \begincasesk(x^2(1-x)) \text for 0 Evaluate k and sketch

Question: Suppose that $X$ is a continuous random variable with probability density of the form

\[f(x)= \begin{cases}k\left(x^{2}(1-x)\right) & \text { for } 0

Evaluate $k$ and sketch a graph of $f(x)$.

Evaluate $P[X \leq .25], P\left[X^{\circ} \leq .75\right], P[.25<$ $X \leq .75]$, and $P[|X-.5|>.1]$

Compute EX and $\sqrt{\operatorname{Var} X}$.

Compute and graph $F(x)$, the cumulative distribution function for X. Read from your graph the .6 quantile of the distribution of $X$.

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(See) Suppose that X is a continuous random variable with probability density of the form f(x)= \begincasesk(x^2(1-x)) \text for 0 Evaluate k and sketch

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