7. The density function of X is given by $$f(x) = begin{cases} a + bx^2 & 0...

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7. The density function of X is given by

$$f(x) = \begin{cases}

a + bx^2 & 0 \le x \le 1 \\

0 & otherwise

\end{cases}$$

If E[X]= $\frac{1}{3}$, find a and b.

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