Question

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.

Answer 1

Answer:

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