Question

In: Statistics and Probability

If electricity power failures occur according to a Poisson distribution with an average of 3 failures...

If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks:

a) Calculate the probability that there will not be more than one failure during a particular week.

b) What is the distribution of the time between power failures?

c) What is the probability that the time between two power failures is between 15 and 30 weeks?

d) What is the probability that the time between two power failures is at least 40 weeks given that it has already been 20 weeks since the last failure?

Solutions

Expert Solution


Related Solutions

Certain electrical disturbances occur according to a Poisson process with rate 3 per hour. These disturbances...
Certain electrical disturbances occur according to a Poisson process with rate 3 per hour. These disturbances cause damage to a computer. a) Assume that a single disturbance will cause the computer to crash. What is the probability that the system will crash in the coming 10 minutes? b) Assume that the computer will survive a single disturbance, but the second such disturbance will cause it to crash. What is, now, the probability that the computer will crash in the coming...
Singapore Power (SP) is the only operator in the domestic electricity market in Singapore. Electricity distribution...
Singapore Power (SP) is the only operator in the domestic electricity market in Singapore. Electricity distribution generally is associated with extremely high economies of scale because of the infrastructure (a nationwide power grid) needed to deliver power to individual households. Using the theory and models of market structure, examine this firm. Should government be worried about any aspect of how a firm under this market structure will perform? What should government do to address such worries?
The number of earthquakes that occur per week in California follows a Poisson distribution with a...
The number of earthquakes that occur per week in California follows a Poisson distribution with a mean of 1.5. (a) What is the probability that an earthquake occurs within the first week? Show by hand and provide the appropriate R code. (b) What is the expected amount of time until an earthquake occurs? (c) What is the standard deviation of the amount of time until two earthquakes occur? (d) What is the probability that it takes more than a month...
A certain electric power company maintains that its average rate of critical home electrical power failures...
A certain electric power company maintains that its average rate of critical home electrical power failures is 1.3 failures per day. From analyzes carried out in previous years, it is known that critical failures appear according to a Poisson process. The failure repair team in electrical networks of that company maintains that the failure rate received per day is higher and chooses to make a count of the number of failures reported to it during the month of May to...
Customers arrive at a department store according to a Poisson process with an average of 12...
Customers arrive at a department store according to a Poisson process with an average of 12 per hour. a. What is the probability that 3 customers arrive between 12:00pm and 12:15pm? b. What is the probability that 3 customers arrive between 12:00pm and 12:15pm and 6 customers arrive between 12:30pm and 1:00pm? c. What is the probability that 3 customers arrive between 12:00pm and 12:15pm or 6 customers arrive between 12:30pm and 1:00pm? d. What is the probability that a...
Customers arrive at a hair salon according to a Poisson process with an average of 16...
Customers arrive at a hair salon according to a Poisson process with an average of 16 customers per hour. The salon has just one worker due to covied-19 restriction. Therefore, the salon must close whenever the worker leaves. assume that customers who arrive while the salon is closed leave immediately and don’t wait until the worker returns. The salon is closed on weekends. a. What is the probability that at most (less than) four customers arrive in the hour before...
Customers arrive in a certain shop according to an approximate Poisson process on the average of...
Customers arrive in a certain shop according to an approximate Poisson process on the average of two every 6 minutes. (a) Using the Poisson distribution calculate the probability of two or more customers arrive in a 2-minute period. (b) Consider X denote number of customers and X follows binomial distribution with parameters n= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period. (c) Let Y denote the waiting time in minutes until...
Suppose the number of customers arriving at a store obeys a Poisson distribution with an average...
Suppose the number of customers arriving at a store obeys a Poisson distribution with an average of λ customers per unit time. That is, if Y is the number of customers arriving in an interval of length t, then Y∼Poisson(λt). Suppose that the store opens at time t=0. Let X be the arrival time of the first customer. Show that X∼Exponential(λ).
Claims arrive to an insurance company according to a Poisson Process. The average number of claims...
Claims arrive to an insurance company according to a Poisson Process. The average number of claims reported every day is 2.5. It has been reported that 15% of these claims are fake. What is the probability that in a week of five business day 10 claims arrive and one of these is fake? ONLY ANSWERRRRR
Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There...
Customers arrive at a cafe every 2 minutes on average according to a Poisson process. There are 2 employees working at the bar providing customer service, i.e., one handling customer orders and another handling payments. It takes an average of 1 minute to complete each order (exponentially distributed). Based on the above: f. What are the service time probability density and cumulative distribution functions? g. What percentage of customer orders will be prepared in exactly 2 minutes? h. What are...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT