An article suggests that a Poisson process can be used to represent the occurren

Question

An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year (a) How many loads can be expected to occur during a 2-year period? loads (b) What is the probability that more than six loads occur during a 2-year period? (Round your answer to three decimal places.) (c) How long must a time period be so that the probability of no loads occurring during that period is at most 0.1? (Round your answer to four decimal places.) 5.7565Xyr

Explanation / Answer

Solution

Let X = number of times loads occur during a 2-year period. Then, we are given X ~ Poisson (), where = average number of times loads occur during a 2-year period = 5 [given inter-load gap is 0.4 year, number of occurrences = 2/0.4 = 5]

Part (b)

Probability of more than 6 loads occurring during a 2-year period

= P(X > 6)

= 0.238 ANSWER [using Excel Function of Poisson Distribution]

Part (c)

We want the period for which P(X = 0) 0.1.

Or e- 0.1 [because for any Poisson variable probability of zero is e-]

Taking log to base ‘e’, - loge0.1

- - 2.30259 [using Excel Function on logarithm]

Or 2.30259

=> average number of occurrences over a 2-year period 2.30259

=> inter-load time 2/2.30259 = 0.8686 year = 10.4230 months ANSWER

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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