The random variable $\xi$ has the following pdf:
$$f(x)=\begin{cases}kx^2&0<x<6\\
0&\text{else}\end{cases}$$
a) determine $k$
b) determine $P(\xi<2)$
I dont know where to start. After looking at an example I started to think that the interval for $\xi$ is [0, 5] and then P($\xi$ $<=x$) = $x/5$ so then k would be $1/5$ but thats very wrong.
The answers are:
a: $1/72$
b:$1/27$
Hint: You need the total probability to sum to one.
$$ \int_{-\infty}^{\infty} f(x) \,dx = \int_0^6 kx^2\,dx = 1 $$
solve for $k$.
For the second part you solve the integral:
$$ \int_0^2 kx^2 \,dx $$
(where you use the $k$ that you found in part a.