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.

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

is should be y = 5x

step-by-step explanation:

correct me if im wrong

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)