Question

Let 𝑋1, 𝑋2,be a sequence of 𝑖. 𝑖. 𝑑. random variables, each having the probability density function
$f(x) =\begin{cases} \frac{x^2r^{-x}}{2} & \quad \text{if }x ≥0,\\\ 0, & \quad Otherwise \end{cases}$
For some real constants 𝛽, 𝛾 and 𝑘, suppose that
$lim_{→∞} ( \frac{1}{ 𝑛} ∑^n_{i=1}𝑋_𝑖≤ 𝑥)$=$\begin{cases} 0 & \quad if\,x< β.\\\ kx, & \quad if\,β≤x≤y.\\\ ky, & \quad if\,x>y.\end{cases}$
Then, the value of 2𝛽 + 3𝛾 + 6𝑘 equals _______

Answer 1

The correct answer is: 17