# Median

### Practice Problem Set 2 – finding median losses

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This post has two practice problems to find the median of a distribution that models insurance losses.

 Practice Problem 2a Losses have a distribution with the following density function: $\displaystyle f(x)=\frac{1}{6} e^{-\frac{x}{12}}-\frac{1}{6} e^{-\frac{x}{6}} \ \ \ x>0$. Calculate the median loss amount.
 Practice Problem 2b Losses are modeled by a distribution that is a mixture of two exponential distributions, one with mean 6 and the other with mean 12. The weight of each distribution is 50%. Calculate the median loss amount.

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Solutions

Problem 2a

Median $\displaystyle =-12 \times \log \biggl(\frac{2-\sqrt{2}}{2} \biggr)=14.7354$

log is logarithm to base $e$ = 2.718281828…

Problem 2b

Median $\displaystyle =-12 \times \log \biggl(\frac{-1+\sqrt{5}}{2} \biggr)=5.7745$

log is logarithm to base $e$ = 2.718281828…

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$\copyright$ 2017 – Dan Ma