Question: Let X be continuous random variable having density function

\[f\left( x \right)=\left\{ \begin{aligned} & C{{x}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,0<x<1 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{elsewhere} \\ \end{aligned} \right.\]

Find: a) Constant C,


b) Cumulative function F(x)


c) Expectation E(X), standard deviation σ.

d) P(X < 1.5), P(X > 1), P(1 < X < 1.5)