# Science:Math Exam Resources/Courses/MATH103/April 2014/Question 03 (c)

MATH103 April 2014
Other MATH103 Exams

### Question 03 (c)

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.]

Assume that the lifetime of a salmon depends on how quickly it manages to reach the Pacific Ocean as a juvenile. Suppose that a salmon lives $s$ years, where $s=\ln(t+1)$ , if it reach the Pacific Ocean in $t$ days. Find the probability density function $q(s)$ for $s$ .

Work must be shown for full marks. Simplify fully.

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