Science:Math Exam Resources/Courses/MATH103/April 2014/Question 03 (b)/Statement

Vancouver has some of the best salmon hatcheries (i. e. salmon farms) in the world. The probability that a young salmon takes $t$ days to swim from the Capilano Salmon Hatcher to the Pacific Ocean is given by the probability density function $p(t)=e^{3-t}$ for $3\leq t\leq \infty$. [It is assumed that it takes at least $3$ days for a salmon to reach the ocean.]

Find the average (i. e. mean) time it takes for a young salmon to swim from the hatchery to the Pacific Ocean.

Work must be shown for full marks. Simplify fully.