Homework SourseSuppose X follow an exponential distribution with mean 10 de
Suppose X follow an exponential distribution with mean 10, determine a) E(10x-5) and b) the 95th percentile,
Use probability density function
Suppose X follow an exponential distribution with mean 10, determine a) E(10x-5) and b) the 95th percentile,
Use probability density function
Use probability density function
Solution
a)
As
E(x) = 10
then
E(10x - 5) = 10E(x) - 5 = 10(10) - 5
E(10x - 5) = 95 [ANSWER]
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b)
Here, the cumulative density function is
F(x) = 1 - exp(-x/10)
Thus, if F(x) = 0.95, finding x,
F(x) = 1 - exp(-x/10)
0.95 = 1 - exp(-x/10)
0.05 = exp(-x/10)
x = -10* ln(0.05) = 29.95732274 [ANSWER, 95TH PERCENTILE]
