Question

Suppose you have a random variable that is uniformly distributed between 7 and 26. what is the expected value for this random variable? answer to one decimal place if necessary.

Answer 1

$\mathbb E(X)=\int_7^{26}\dfracx{26-7}\,\mathrm dx=\dfrac{33}2=16.5$

which follows from the definition for expected value,

$\mathbb E(X)=\int_{-\infty}^\infty xf_X(x)\,\mathrm dx$

where $f_X(x)$ is the probability density function for $X$.