4 The time to failure of a certain type of electrical compon

4. The time to failure of a certain type of electrical component is assumed to follow an all al distribution with a mean of 4 years. The manufacturer replaces free components that fail while under guarantee a) What is the probability that a component will fail in 1 year? b) What is the probability that a component will fail between 2 and 4 years?

Solution

Solution:

We have given, random variable X: Time to failure for a certail electrical component.

X follows exponential distribution with mean = 4

a) We need to compute Pr(X1). Therefore, the following is obtained:

Pr(X1)=1–e^1/4=0.2212

Using excel, ........ =EXPONDIST(1,1/4,TRUE)

b) We need to compute Pr( 2 X 4). Therefore, the following is obtained:

Pr(2 X 4)=Pr( X 4 ) – Pr ( X 2 )

=e^2/4 – e^4/4 = 0.6065 – 0.3679 = 0.2386

Done