Question

Suppose you have a random variable that is uniformly distributed between 1 and 29. what is the expected value for this random variable?

Answer 1

Assuming the distribution is continuous, you have


`\mathbb E(X)=\displaystyle\int_1^(29)\frac x{29-1}\,\mathrm dx=\frac1{28}\int_1^(29)x\,\mathrm dx=15`

If instead the distribution is discrete, the value will depend on how the interval of number between 1 and 29 are chosen - are they integers? evenly spaced rationals? etc