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
