Ask Question
14 December, 05:18

Use two different computations (one involving the Poisson and another the exponential random variable) to determine the probability that no job will arrive during the next 15 minutes.

+4
Answers (1)
  1. 14 December, 05:21
    0
    Probability according to Poisson's distribution function = 0.04979

    Probability according to Exponential random variable = 0.3333

    Step-by-step explanation:

    In 15 minutes, the number of jobs that arrive on the average = (12/60) * 15 = 3 jobs per 15 minutes

    Poisson distribution formula is given as

    P (X = x) = (e^-λ) (λˣ) / x!

    λ = mean = 3 jobs per 15 minutes

    x = variable whose probability is required = 0

    P (X = 0) = (e⁻³) (3⁰) / 0! = 0.04979

    Exponential random variable formula is given by

    P (X=x) = f (x,λ) = λ e^ (-λ. x)

    λ = rate parameter, that is, time between jobs.

    λ = (1/3) (15 minutes per job) = 0.3333

    P (X = 0) = f (0, 0.3333) = 0.3333 e^0 = 0.3333
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Use two different computations (one involving the Poisson and another the exponential random variable) to determine the probability that no ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers