Suppose female customers come to a shop according to a Poisson process of rate λ per...
Suppose female customers come to a shop according to a Poisson process of rate λ per hour and male customers according to an independent Poisson process of rate µ per hour. a) What is the conditional distribution of the total number of female customers coming to the shop in the first hour given that the total number of customers coming to the shop in the first hour is n? b) What is the probability that the first customer coming to the shop is female?
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Suppose female customers come to a shop according to a Poisson
process of rate λ per...
Customers enter a store according to a Poisson process of rate λ = 5 per hour....
Customers enter a store according to a Poisson process of rate λ = 5 per hour. Independently, each customer buys something with probability p = 0.8 and leaves without making a purchase with probability q = 1 − p = 0.2. Each customer buying something will spend an amount of money uniformly distributed between $1 and $101 (independently of the purchases of the other customers). What are the mean and the standard deviation of the total amount of money spent...
Customers arrive at a bank according to a Poisson process having a rate of 2.42 customers...
Customers arrive at a bank according to a Poisson process having a rate of 2.42 customers per hour. Suppose we begin observing the bank at some point in time. What is the probability that 3 customers arrive in the first 1.8 hours? Customers arrive at a bank according to a Poisson process having a rate of 2.3 customers per hour. Suppose we begin observing the bank at some point in time. What is the expected value of the number of...
Customers arrive at a service facility according to a Poisson process of rate 5/hour. Let N(t)...
Customers arrive at a service facility according to a Poisson process of rate 5/hour. Let N(t) be the number of customers that have arrived up to time t (t hours) a. What is the probability that there is at least 2 customer walked in 30 mins? b. If there was no customer in the first 30 minutes, what is the probability that you have to wait in total of more than 1 hours for the 1st customer to show up?...
Customers arrive at a bank at a Poisson rate λ. Suppose two customers arrived during the first ho...
Please give a detailed answer
Customers arrive at a bank at a Poisson rate λ. Suppose two customers arrived during the first hour. What is the probability that (a) both arrived during the first 20 minutes? (b) at least one arrived during the first 20 minutes?
Customers arrive at a bank at a Poisson rate λ. Suppose two customers arrived during the first hour. What is the probability that (a) both arrived during the first 20 minutes? (b) at least...
Customers are arriving to a shop according to Poisson process with mean 3 customers/hour. What is...
Customers are arriving to a shop according to Poisson process with mean 3 customers/hour. What is the probability that only 5 customers will arrive next two hours?
customers arrive according to a Poisson process at rate λ > 0. Assume that service crew...
customers arrive according to a Poisson process at rate λ > 0. Assume that service crew start serving a service and it takes a fixed amount of time τ to serve. For t ≧ 0, let X(t) denote the number of customers being served at time t. What is the distribution of X(t)? What is E[X(t)]?
Number of customers coming to a massage parlor follows a Poisson distribution with 1 = 4...
Number of customers coming to a massage parlor follows a Poisson distribution with 1 = 4 customers per hour. Let the amount spent (in dollars) by a customer be distributed as N(80, 900). a.(4 points) If the shop opens at 9 am, what is the probability that the first customer arrives between 9:30 am and 10 am? b. (8 points) What is the probability that the parlor makes a revenue of more than $100 within an hour of its opening?...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at ...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds (a) Find L, Lq, W, and W (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and W
Problem 4. Marsha operates an expresso...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
Suppose that visits to a website can be modeled by a Poisson process with a rate λ=10 per hour (a...
suppose that visits to a website can be modeled by a Poisson
process with a rate λ=10 per hour
(a) What is the probability that there are more than or equal to
2 visits within a given 1/2 hour interval
(b) A supervisor starts to monitor the website from the start of
a new shift. then what is the expected value of time waited by the
supervisor until the 10th visit to the website during that
shift?
Suppose that visits...
Customers arrive at a service facility according to a Poisson process of rate 5/hour. Let N(t) be the number of customers that have arrived up to time t (t hours) a. What is the probability that there is at least 2 customer walked in 30 mins? b. If there was no customer in the first 30 minutes, what is the probability that you have to wait in total of more than 1 hours for the 1st customer to show up?...
Please give a detailed answer
Customers arrive at a bank at a Poisson rate λ. Suppose two customers arrived during the first hour. What is the probability that (a) both arrived during the first 20 minutes? (b) at least one arrived during the first 20 minutes?
Customers arrive at a bank at a Poisson rate λ. Suppose two customers arrived during the first hour. What is the probability that (a) both arrived during the first 20 minutes? (b) at least...
Customers are arriving to a shop according to Poisson process with mean 3 customers/hour. What is the probability that only 5 customers will arrive next two hours?
Number of customers coming to a massage parlor follows a Poisson distribution with 1 = 4 customers per hour. Let the amount spent (in dollars) by a customer be distributed as N(80, 900). a.(4 points) If the shop opens at 9 am, what is the probability that the first customer arrives between 9:30 am and 10 am? b. (8 points) What is the probability that the parlor makes a revenue of more than $100 within an hour of its opening?...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds (a) Find L, Lq, W, and W (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and W
Problem 4. Marsha operates an expresso...
suppose that visits to a website can be modeled by a Poisson
process with a rate λ=10 per hour
(a) What is the probability that there are more than or equal to
2 visits within a given 1/2 hour interval
(b) A supervisor starts to monitor the website from the start of
a new shift. then what is the expected value of time waited by the
supervisor until the 10th visit to the website during that
shift?
Suppose that visits...
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