The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. You have owned this CPU for three years. a. What is the probability that the CPU fails in the next three years? 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?

This question is based on the probability. Therefore, the probability that the CPU fails in the next three years is 0.393  and  the probability that at least one fails within the next three years is 0.993.

Given:

The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. You have owned this CPU for three years.

(a) We need to determined the probability that the CPU fails in the next three year.

It is given that, mean of exponential distribution = 6

By using Poisson distribution:

P(X =x) Probability of failure in next 3 years :

(b) We need to determined the probability that at least one fails within the next three years.

Number of pc owned = 10 ; n = 10

P(at least 1 fails) :

Therefore, the probability that the CPU fails in the next three years is 0.393  and  the probability that at least one fails within the next three years is 0.993.

For more details, prefer this link:

link

0.39 ; 0.993

Step-by-step explanation:

Given that:

Mean of exponential distribution = 6

Using poisson :

P(X =x)Probability of failure in next 3 years :

Number of occurrences λ = 1 / 6 = 0.1667

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 - 0.60653

P(X < 3) = 0.39346

= 0.393

B.)

Number of pc owned = 10 ; n = 10

P(atleast 1 fails) :

P(X ≥ 3)^n = 1 - [1 - P(X < 3)] ^n

P(X ≥ 3)^n = 1 - (1 - 0.393)^10

P(X ≥ 3)^n = 1 - 0.607^10

= 1 - 0.00679

= 0.993

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent

about 0.75 hours

step-by-step explanation: