Question: 4. The random variable X has probability density function $$ f(x) = begin{cases} ax + bx^2 & 0 < x < 1 0 &

4. The random variable X has probability density function

$$

f(x) = \begin{cases}

ax + bx^2 & 0 < x < 1 \\

0 & otherwise

\end{cases}

$$

If E[X] = 6, find

(a) P{X ≤ 1/2} and

(b) Var(X).

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