Independent solution

How to solve this Exponential Distribution question

Setup

Setup

Let beta denote the exponential mean. Its variance is beta squared.

β2=7225\beta^2=7225
β=85\beta=85

Model

Model

The median m leaves survival probability one half.

e−m/β=12e^{-m/\beta}=\frac12
m=βln⁡2=85ln⁡2m=\beta\ln2=85\ln2

Compute

Compute

Subtract the mean from the median in the requested order.

m−E⁡[X]=85ln⁡2−85m-\operatorname{E}[X]=85\ln2-85
85(ln⁡2−1)=−26.082489652485(\ln2-1)=-26.0824896524

Answer

Answer

The median is approximately 26 units below the mean.

−26(B)\boxed{-26\quad\text{(B)}}