December I8, 2017 Math 311 Final Exam, Page 5 of S A company models insurance cl

Question

December I8, 2017 Math 311 Final Exam, Page 5 of S A company models insurance claims as a Poisson process, assuming that claims will arrive at random at a rate of I per day ts) 5. What is the probability that there are no claims on January Ist (b) What is the probability that there are exactly 300 claims total in 2017 (c) Suppose that the last claim was precisely 1.25 days ago. Given this information, what is the probability that the total time between the last claim and the next claim is greater than 2.25? d) Let X be the number of days starting January 1st until the first day where at least two chins occur. (For example, If January 3rd is the first day with two claims, then X-2) What is E(X)?

Explanation / Answer

Here = 1 per day

So we haver to first find the probability of at least two claims occur on any given day. If Y is the number of claims occur on any given day.

So,

Pr(Y>= 2 ) = POISSON (Y > = 2) = 1 - [Pr( Y= 0; 1) + Pr(Y = 1; 1) ]

= 1 - [e-1 0!/0! + e-1 1!/1!]

= 1- (0.3679 + 0.3679) = 0.2642

so now here p = 0.2642 for atleast 2 claims occur. Now the random variable X is the number of days starting january 1st until the first day where at least two claim occur. That is a geometric distriburtion with success probability p = 0.2642

So E(X + 1) = 1/p = 1/0.2642 = 3.7844

E(X) = 3.7844 - 1 = 2.7844

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

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