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

Correct Answer: 17

The correct answer is: 17