The number of customers entering a store on a given day is Poisson distributed with mean...
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.
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The number of customers entering a store on a given day is
Poisson distributed with mean...
5. The number of customers entering a store on a given day is a random variable...
5. The number of customers entering a store on a given day is a random variable N with mean a > 0 and variance b > 0. The amount of money spent by customer i is a random variable Xi with mean c0 and variance d2 〉 0. The m ean c and variance d2 are the same for all customers. The variables X2, are independent across the customers and are also independent of N. Find the correlation of N...
2. The number of customers entering Heal's in a given hour is Poisson distributed with mean...
2. The number of customers entering Heal's in a given hour is Poisson distributed with mean 30. The amount of money (in pounds) spent by each customer is uniformly distributed over (0, 500). Let T denote the total amount of money spent by customers in Heal's in one hour. Find ET). You should define any notation you use and note any assumptions you make. HINT 1: Write T as a sum of random variables, noting that the number of random...
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...
4. Freebirds in IV receives N customers per day, where N is a random variable with...
4. Freebirds in IV receives N customers per day, where
N is a random variable with mean 200
and standard deviation 40. The amount spent by each customer is
normally distributed with
mean $15 and standard deviation $3. The amounts that customers
spend are independent of
each other and independent of N. Find the mean and variance of the
total amount spent at
Freebirds per day.
1. Freebirds in IV receives N customers per day, where N is a random...
The number of automobiles entering a tunnel per 2-minute period follows a Poisson distribution. The mean...
The number of automobiles entering a tunnel per 2-minute period follows a Poisson distribution. The mean number of automobiles entering a tunnel per 2-minute period is four. (A) Find the probability that the number of automobiles entering the tunnel during a 2minute period exceeds one. (B) Assume that the tunnel is observed during four 2-minute intervals, thus giving 4 independent observations, X1, X2, X3, X4, on a Poisson random variable. Find the probability that the number of automobiles entering the...
(1 point) You are interested in finding out the mean number of customers entering a 24-hour convenience store every 10-...
(1 point) You are interested in finding out the mean number of customers entering a 24-hour convenience store every 10-minutes. You suspect this can be modeled by the Poisson distribution with a a mean of = 3.59 customers. You are to randomly pick n = 57 10-minute time frames, and observe the number of customers who enter the convenience store in each. After which, you are to average the 57 counts you have. That is, compute the value of X...
(5.) You run a store that sells Christmas trees for Sd each. Suppose the number of...
(5.) You run a store that sells Christmas trees for Sd each. Suppose the number of customers that enter your store on a given day is described by a Poisson random variable with parameter λ. Further, suppose that each customer buys a tree with probability p, and that all customers are independent. (a) What is the expected number of customers that enter your store on a given day? (b) What is your expected revenue for a single day (revenue is...
Let n be the unknown number of customers that visit a store on the day of...
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...
A store is about to close for the day. There are still two (unrelated) customers in the store. We estimate that it takes 10 minutes for a customer to exit the store. What is the probability that it wo...
A store is about to close for the day. There are still two (unrelated) customers in the store. We estimate that it takes 10 minutes for a customer to exit the store. What is the probability that it would take more than 20 minutes for the last customer to leave the store?
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?...
5. The number of customers entering a store on a given day is a random variable N with mean a > 0 and variance b > 0. The amount of money spent by customer i is a random variable Xi with mean c0 and variance d2 〉 0. The m ean c and variance d2 are the same for all customers. The variables X2, are independent across the customers and are also independent of N. Find the correlation of N...
2. The number of customers entering Heal's in a given hour is Poisson distributed with mean 30. The amount of money (in pounds) spent by each customer is uniformly distributed over (0, 500). Let T denote the total amount of money spent by customers in Heal's in one hour. Find ET). You should define any notation you use and note any assumptions you make. HINT 1: Write T as a sum of random variables, noting that the number of random...
4. Freebirds in IV receives N customers per day, where
N is a random variable with mean 200
and standard deviation 40. The amount spent by each customer is
normally distributed with
mean $15 and standard deviation $3. The amounts that customers
spend are independent of
each other and independent of N. Find the mean and variance of the
total amount spent at
Freebirds per day.
1. Freebirds in IV receives N customers per day, where N is a random...
(1 point) You are interested in finding out the mean number of customers entering a 24-hour convenience store every 10-minutes. You suspect this can be modeled by the Poisson distribution with a a mean of = 3.59 customers. You are to randomly pick n = 57 10-minute time frames, and observe the number of customers who enter the convenience store in each. After which, you are to average the 57 counts you have. That is, compute the value of X...
(5.) You run a store that sells Christmas trees for Sd each. Suppose the number of customers that enter your store on a given day is described by a Poisson random variable with parameter λ. Further, suppose that each customer buys a tree with probability p, and that all customers are independent. (a) What is the expected number of customers that enter your store on a given day? (b) What is your expected revenue for a single day (revenue is...
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?...
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