Question

In: Statistics and Probability

Define the Poisson distribution when you are interested in the number of times an event occurs...

Define the Poisson distribution when you are interested in the number of times an event occurs in a given area of opportunity.

Elaborate how the Area of opportunity is a continuous unit or interval of time, volume, or such area in which more than one occurrence of an event can occur?

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Define the Poisson distribution when you are interested in the number of times an event occurs...
Define the Poisson distribution when you are interested in the number of times an event occurs in a given area of opportunity. Elaborate how the Area of opportunity is a continuous unit or interval of time, volume, or such area in which more than one occurrence of an event can occur?
A fair die is rolled 20 times. We define Ai as the event that number i...
A fair die is rolled 20 times. We define Ai as the event that number i appears i times (i = 1, ..., 6). (a) Calculate P(Ai) for all i. (b) Calculate P(Ai ∩ Aj) for all i ̸= j. (c) Calculate P(A1 ∩A2 ∩A3 ∩A4 ∩A5 ∩A6). (d) Calculate P(A2 ∩A3 ∩A4 ∩A5 ∩A6).
A fair die is rolled 20 times. We define Ai as the event that number i...
A fair die is rolled 20 times. We define Ai as the event that number i appears i times (i = 1, ..., 6). (a) Calculate P(Ai) for all i. (b) Calculate P(Ai ∩ Aj) for all i ̸= j. (c) Calculate P(A1 ∩A2 ∩A3 ∩A4 ∩A5 ∩A6). (d) Calculate P(A2 ∩A3 ∩A4 ∩A5 ∩A6).
The number of imperfections in an object has a Poisson distribution with a mean λ =...
The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad...
The number of arriving customers to a big supermarket is following a Poisson distribution with a...
The number of arriving customers to a big supermarket is following a Poisson distribution with a rate of 4 customers per a minute. What is the probability that no customer will arrive in a given minute? What is the probability that exactly 3 customers will arrive in a given minute? What is the probability that at least seven customer will arrive in a given minute? What is the probability that at most one customer will arrive in 40 seconds? What...
The number of views of a page on a Web site follows a Poisson distribution with...
The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. (i) What is the probability of no views in a minute? (ii) What is the probability of two or fewer views in 10 minutes? (iii) What is the probability of two or fewer views in 2 hours?
The number of airplane landings at a small airport follows a Poisson distribution with a mean...
The number of airplane landings at a small airport follows a Poisson distribution with a mean rate of 3 landings every hour. 4.1 (6%) Compute the probability that 3 airplanes arrive in a given hour? 4.2 (7%) What is the probability that 8 airplanes arrive in three hours? 4.3 (7%) What is the probability that more than 3 airplanes arrive in a period of two hours?
The cell number of a senator was published on Twitter. Following a Poisson distribution, the rate...
The cell number of a senator was published on Twitter. Following a Poisson distribution, the rate at which calls were coming through was 1.5 per minute. a. What is the probability that no call came through in a one-minute period? b. What is the probability that less than 180 calls came through in a two-hour period?
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an...
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an average rate of 2 earthquakes every year. a.) Find the probability that there will be 1 to 3 (inclusive) earthquakes during the next year in this area. b.) Find the probability that there will be exactly 5 earthquakes during the next 3 year period. c.) Consider 10 randomly selected years during last century. What is the probability that there will be at least 3...
The number of people arriving at an emergency room follows a Poisson distribution with a rate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate of 9 people per hour. a) What is the probability that exactly 7 patients will arrive during the next hour? b. What is the probability that at least 7 patients will arrive during the next hour? c. How many people do you expect to arrive in the next two hours? d. One in four patients who come to the emergency room in hospital. Calculate...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT