Answer :
Given probability = p
therefore,probability distribution of the number of purchasing customers in a day is :
Exponential distribution with
5.90 During any particular day, the number of customers that arrive at Grandma's Fudge Shoppe has...
Customers arrive at Lisa’s Hair Salon during a day in any particular business hour according to a Poisson distribution with a rate of ? = 3 per hour. Now the salon has two barbers who can each service a customer in exactly 30 minutes. Suppose a customer, Amy, arrives at 2:00pm and finds both barbers idle. (a) What is the probability that we will observe customers waiting before 2:30pm? (b) What is the probability that Amy observes the next customer...
The number of customers entering a store on a given day is Poisson distributed with mean 150 . The amount spent in the store by a customer is exponential with mean 200. The amount spent is independent from number of customers . Estimate the probability that the store takes in at least $20,000. Leave the answer in terms of the distribution of he standard normal random variable.
Let n be the unknown number of customers that visit a store on the day of a sale. The number of customers that make a purchase is Y | n ~ Binomial(n, theta) where theta is the known probability of making a purchase given the customer visited the store. The prior is n ~ Poisson(5). Assuming theta is known and n is the known parameter, plot the posterior distribution of n for all combinations of Y=0,5,10 and theta=0.2,0.5 and comment...
Customers arrive at a pet store at a rate of 3/hr. The number of customers between Dog-buyers Y satisfies P (Y = i − 1) = 1/3 (2/3)^(i − 1), i = 1, 2, 3,... meaning, if customer c buys a dog, then the probability the next Dog-buying customer is customer (c + i) is 1/3 (2/3)^(i − 1). Of those that buy dogs, 1/4 buy Cockapoos. What is the probability that 5 Cockapoos will be sold in a 12...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Please answer all parts a-c. Thanks. 5 Boutique Store Consider a boutique store in a busy shopping mall. Every hour, a large number of people visit the mall, and each independently enters the boutique store with some small probability. The store owner decides to model X, the number of customers that enter her store during a particular hour, as a Poisson random variable with mean 2. Suppose that whenever a customer enters the boutique store, they leave the shop without...
A small market has two checkout lines, regular and express. Let X be the number of customers in line at a regular checkout, and Y that at the express checkout. At a particular time of the day, the joint probability mass function of X and Y is given by (a) Find the probability that the total number of customers at a given time is at most 1, that is find P(X+Y≤1) [1] (b) Fill in the table with the marginal distribution of...
Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of three hours from the time that the customer notifies OEI of an equipment problem. Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all...