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

$f_X(x)=\begin{cases}\dfrac1{45-20}=\dfrac1{25}&\text{for }20\le x\le45\\0&\text{otherwise}\end{cases}$

The mean is given by

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