$ f(x) = \begin{cases} k\sqrt{x}, 0
I know that $E[X] = \frac{2k}{5}$ and $Var[X] = \frac {2k}{7}$
Then what can I do to find $k$ with these few information?
$ f(x) = \begin{cases} k\sqrt{x}, 0
I know that $E[X] = \frac{2k}{5}$ and $Var[X] = \frac {2k}{7}$
Then what can I do to find $k$ with these few information?
Updated to match the corrected version of the question:
You must have $\int_{-\infty}^\infty f(x)~dx=1$ in order for $f$ to be a probability density function. In this case
$\int_{-\infty}^\infty f(x)~dx=\int_0^1 k\sqrt x~dx=k\int_0^1 x^{1/2}~dx\;,$
so you need only solve the equation
$k\int_0^1 x^{1/2}~dx=1$
for $k$.