SOA Exam FAM Sample Question 13
Study guide: Exam FAM
Losses come from a mixture of an exponential distribution with mean 100 with probability p and an exponential distribution with mean 10,000 with probability 1 - p.
Losses of 100 and 2000 are observed.
Determine the likelihood function of p.
- A)
\left(\dfrac{pe^{-1}}{100}\cdot\dfrac{(1-p)e^{-0.01}}{10{,}000}\right)\cdot\left(\dfrac{pe^{-20}}{100}\cdot\dfrac{(1-p)e^{-0.2}}{10{,}000}\right) - B)
\left(\dfrac{pe^{-1}}{100}\cdot\dfrac{(1-p)e^{-0.01}}{10{,}000}\right)+\left(\dfrac{pe^{-20}}{100}\cdot\dfrac{(1-p)e^{-0.2}}{10{,}000}\right) - C)
\left(\dfrac{pe^{-1}}{100}+\dfrac{(1-p)e^{-0.01}}{10{,}000}\right)\cdot\left(\dfrac{pe^{-20}}{100}+\dfrac{(1-p)e^{-0.2}}{10{,}000}\right) - D)
\left(\dfrac{pe^{-1}}{100}+\dfrac{(1-p)e^{-0.01}}{10{,}000}\right)+\left(\dfrac{pe^{-20}}{100}+\dfrac{(1-p)e^{-0.2}}{10{,}000}\right) - E)
p\left(\dfrac{e^{-1}}{100}+\dfrac{e^{-0.01}}{10{,}000}\right)+(1-p)\left(\dfrac{e^{-20}}{100}+\dfrac{e^{-0.2}}{10{,}000}\right)
Answer this question and see the worked solution