Question

The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years.

Answer 1

Answer: 0.393 ; 0.9933

Step-by-step explanation:

Given that :

Mean lifetime follows an exponential distribution (m) = 6

a. What is the probability that the CPU fails in the next three years?

Using the poisson distribution formula :

1 - e^-λt

λ = 1/m = 1 / 6 = 0.1667

Probability of failure in next 3 years :

P(X < 3) = 1 - e^-λx

P(X < 3) = 1 - e^-0.1667*3

P(X < 3) = (1 - e^-0.5)

P(X < 3) = 1 - 0.6065306

P(X < 3) = 0.3934693

= 0.3935

b. Assume that your corporation has owned 10 CPUs for three years, and assume that the CPUs fail independently. What is the probability that at least one fails within the next three years?

Number of pc owned = 10

CPU failure is indepndent

Probability of atleast one fails :

1 - P(X ≥ 3)^n

P(X ≥ 3) = 1 - P(X < 3)

P(X ≥ 3) = 1 - 0.3935 = 0.607

Hence,

1 - P(X ≥ 3) = 1 - 0.6065^10

1 - P(X ≥ 3) = 1 - 0.0067345

1 - P(X ≥ 3) = 0.993265

= 0.9933