Question

Calculate the exponential distribution, expected value, and variance of the given data.

μ = 2, x₁ = 4, x₂ = 1

Answer 1

$f(x,\mu)=x = \begin{cases} \mu e^{-\mu x}&\text{if } x\ge0 \\ 0 &\text{if } x<0 \end{cases}$

$P(1<x<4)=\int^4_12e^{-4x}dx=-\frac{1}{2}(e^{-16}-e^{-4})=0.00916$

$E(X)=1/\mu=1/2$

$V(X)=1/\mu^2=1/4$