I have exams comming up, so practice exam is what i am doing.. however they dont give solutions which is a pain.. anyone care to solve this question because i get stuck.. umm at the start?
The random variable $\displaystyle X$ has density:
$\displaystyle
f_X(x) = \left\{ \begin{array}{cc}
x^2, & \mbox{ for } 0 < x < k \\
0, & \mbox{ for } x<0,\mbox{ or } x>k
\end{array}\right.
$
1. Find the constant $\displaystyle k$.
To be a density we need $\displaystyle \int_0^k x^2 dx = 1$, so find the k
which dose this.