Answer:
Option E - 1000
Step-by-step explanation:
Let X stand for actual losses incurred.
Given that X follows an exponential distribution with mean 300,
To find the 95-th percentile of all claims that exceed 100.
In other words,
0.95 = Pr (100 < x < p95 ) / P(X > 100)
= Fx( P95) − Fx(100 ) / 1− Fx (100)
, where Fx is the cumulative distribution function of X
since, Fx(x) = 1 - e^ (-x/300)
0.95 = 1 - e^ (-P95/300) - [ 1 - e^ ( -100/300) ] / 1 - [ 1 - e^ ( -100/300) ]
= e^ ( -1/3 ) - e^ ( - P95//300) / e^(-1/3)
= 1 - e^1/3 e^ (-P95/300)
The solution is given by , e^ ( - P95/300) = 0.05e^(-1/3)
P95 = -300 ln ( 0.05e^(-1/3) )
= 999
= 1000
