Independent solution

How to solve this Exponential Distribution question

Setup

Setup

Convert the long-run event frequency to an annual exponential rate.

λ=54=1.25 per year\lambda=\frac54=1.25\ \text{per year}
E⁡[T]=1λ=0.8 year\operatorname{E}[T]=\frac1\lambda=0.8\ \text{year}

Model

Model

At the median, the exponential survival probability equals one half.

Pr⁡(T>m)=e−λm=0.5\Pr(T>m)=e^{-\lambda m}=0.5

Compute

Compute

Solve the survival equation for m.

m=ln⁡21.25=0.8ln⁡2=0.5545177m=\frac{\ln 2}{1.25}=0.8\ln2=0.5545177

Answer

Answer

The median waiting time rounds to 0.55 year.

0.55(A)\boxed{0.55\quad\text{(A)}}