Automobiles arrive at a vehicle equipment inspection to a Poisson process with r

Question

Automobiles arrive at a vehicle equipment inspection to a Poisson process with rate of 10 per hour. a. What is the probability that there are at most 6 vehicles coming to the inspection during an hour? b. What is the probability that there are at least 6 vehicles coming to the inspection during an hour? c. What is the probability that there are exactly 6 vehicles coming to the inspection during an hour? Consider the joint pmf of X and Y, f(x, y) = x +2y/18; x = 1, 2 y = 1, 2. Calculate marginal pmfs of X and Y.

Explanation / Answer

3)

we know that the poisson distibution formula is given as

P(x; ) = (e-) (x) / x!

where x is the actual number of successes that result from the experiment, and eis approximately equal to 2.71828 and mu is the mean so here mean = 10

a) at most 6 inspection means that

P(X<=6) = P0 +P1 +P2 + ..... P6

So we put mu = 10 and x = 0 , 1 ,2,3,4,5,6 and solve the equation to get the value as 0.1301

b)

atleast 6 can be calculated as

1 - P(X<6)

1 - (P0 +P1 +P2 .... P5)

1-0.0670 = 0.933

c)

P(X=6)

P(x; ) = (e-10) (106) / 6! = 0.0630

Please note that we can answer only 1 full question at a time , as per the answering guidelines

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.