7. A continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = \begin{cases} k \left( x ^ { 2 } + 2 x + 1 \right) & - 1 \leq x \leq 0
0 , & \text { otherwise } \end{cases}$$
where \(k\) is a positive integer.
- Show that \(k = 3\).
Find
- \(\mathrm { E } ( X )\),
- the cumulative distribution function \(\mathrm { F } ( x )\),
- \(\mathrm { P } ( - 0.3 < X < 0.3 )\).
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