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.

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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

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

what is the original number? you forgot to add it.