The waiting time h (in hours) between each telephone call a person receives is random with the density function $f\left(h\right)=2e^{-2h}\:for\:h\ge 0$
Question: Find the expected time between calls and find the corresponding variance.
I am pretty much clueless on this question, I thought I could use this $V\left(a_1x_1+a_2+x_2\right)\:$
to find the variance, but for some reason, things are not adding up.
Best Answer
Hint: Suppose $H$ is the random variable for the waiting time between each telephone call a person receives with the corresponding density function $f(h)$. Then
$$Var(H)=\mathbb E\left(H^2\right)-\left[\mathbb E\left(H\right)\right]^2=\int\limits_0^{\infty} h^2\cdot 2e^{-2h} \, dh-\left[\int\limits_0^{\infty} h\cdot 2e^{-2h} \, dh\right]^2 $$