Question

Based on the shifted exponential distribution, what is the probability in [%] that a single power plant will fail after 5 years, if its average life expectancy is 7 years and its minimum guaranteed life expectancy is 4 years?

Answer 1

The shifted exponential distribution has a pdf that can be written as

f(0) = le-(1-) for x > 0

Since the minimum guaranteed life expectancy is 4 years,

$\theta = 4$

X E[X] =/ xf () dr = cle-2-0 dr roove vo (y + 6 xe- du = 5*yde-$ydy + Ⓡoxe=avdy JO

We know that the average life expectancy = 7

> co v +

P(Single plant will fail after 5 years) = P(life is less than 5 years) = P(X < 5)

P(X <5) = scade = 1.* dr 3 J4 3 4 5 24/3 e-2/3 = 31-1/3) 37-1/3) (-1/3) =e4/3e-4/3 - e-5/31 = 1-4/3e-5/3 = 0.2835

P(X<5) = 0.2835