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5. The number of customers entering a store on a given day is a random variable...
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.
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...
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...
(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...
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...
A store offers a new seasonal featured product. Let N be the random variable which designates...
A store offers a new seasonal featured product. Let N be the random variable which designates the number of customers who come to the store during the season, where N ∼ Poi (30). It is estimated that the probability that a customer will buy this new product is 0,7 and this independently of one customer to another. a) It is assumed here that the store has an unlimited stock of this product. Let X and Y be the random variables...
Service time for a customer coming through a checkout counter in a retail store is a...
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 1.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n1=41 customers in the first line and n2=51 customers in the second line. a.Compute the mean and the variance of X1 bar−?2 bar. b.Find the probability that the...
The number of fish that a fisherman catches in a day is a Poisson random variable...
The number of fish that a fisherman catches in a day is a Poisson random variable with mean = 30. However, on average, the fisherman throws back two out of every three fish he catches. (a) What is the probability that, on a given day, the fisherman takes home n fish. (b) What is the mean and variance of the number of fish he catches (c) What is the mean and variance of the number of fish he takes home...
5. (15 points) The shopping times of n = 64 randomly selected customers at a local...
5. (15 points) The shopping times of n = 64 randomly selected customers at a local supermarket were recorded. The average and variance of the 64 shopping times were 33 minutes and 356 minutes, respectively. Estimate u, the true average shopping time per customer, with a confidence coefficient of 1-a = 0.90. 6. (10 points) Let X1, X2, ..., Xn denote n independent and identically distributed Bernoulli random vari- ables s.t. P(X; = 1) = p and P(Xi = 0)...
1. Let Xi, X2,... be independent random variables each with the standard normal distribution, and for...
1. Let Xi, X2,... be independent random variables each with the standard normal distribution, and for each n 2 0 let Sn-1 Xi. Use importance sampling to obtain good estimates for each of the following probabilities: (a) Pfmaxn<100 Sn> 10; and (b) Pímaxns100 Sn > 30) HINTS: The basic identity of importance sampling implies that d.P n100 where Po is the probability measure under which the random variables Xi, X2,... are independent normals with mean 0 amd variance 1. The...
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...
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...
(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...
5. (15 points) The shopping times of n = 64 randomly selected customers at a local supermarket were recorded. The average and variance of the 64 shopping times were 33 minutes and 356 minutes, respectively. Estimate u, the true average shopping time per customer, with a confidence coefficient of 1-a = 0.90. 6. (10 points) Let X1, X2, ..., Xn denote n independent and identically distributed Bernoulli random vari- ables s.t. P(X; = 1) = p and P(Xi = 0)...
1. Let Xi, X2,... be independent random variables each with the standard normal distribution, and for each n 2 0 let Sn-1 Xi. Use importance sampling to obtain good estimates for each of the following probabilities: (a) Pfmaxn<100 Sn> 10; and (b) Pímaxns100 Sn > 30) HINTS: The basic identity of importance sampling implies that d.P n100 where Po is the probability measure under which the random variables Xi, X2,... are independent normals with mean 0 amd variance 1. The...
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