Question: If the probability density of a random variable is given by [f(x)= begin{cases}(k+2) x^{3} & 0

If the probability density of a random variable is given by

\[f(x)= \begin{cases}(k+2) x^{3} & 0

find the value \(k\) and the probability that the random variable takes on a value

(a) greater than \(\frac{3}{4}\);

(b) between \(\frac{1}{3}\) and \(\frac{2}{3}\).

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