Question

A random variable x is best described by a continuous uniform distribution from 20 to 45 inclusive. the mean of this distribution is

Answer 1

`f_X(x)=\begin{cases}\frac1{45-20}=\frac1{25}&\text{for }20\le x\le45\\0&\text{otherwise}\end{cases}`

The mean is given by


`\displaystyle\mathbb E(X)=\int_(-\infty)^\infty x f_X(x)\,\mathrm dx=\int_(20)^(45)\frac x{25}\,\mathrm dx=\frac{65}2`