Travel Time between 30 and 45 minutes, variance of travel time?

[Malone Kevins]

If the travel time for a student to get to college is between 30 and 45 minutes, uniformly distributed, the variance of her travel time is?

I found this question in an old statistics exam paper, there was no answer included. Thank you to whoever is able to solve this for me, I'm not to sure of the process of how to solve this myself.

 

[LCKurtz]

Try using [MATH]\sigma^2 = E(X^2) - (E(X))^2[/MATH]

 

[Romsek]

\(\displaystyle t \sim U[30,45]\)

\(\displaystyle E[t] = \displaystyle \int_{30}^{45}\dfrac{t}{45-30}~dt\)

\(\displaystyle E[t^2] = \displaystyle \int_{30}^{45}\dfrac{t^2}{45-30}~dt\)

\(\displaystyle Var[t] = E[t^2]-(E[t])^2\) as noted above.