e. What is $ P(Y = 15) $? **Problem 6: Statistical Order Analysis**A company's marketing department claims that the number of orders placed using their e-commerce store follows a Poisson distribution with a mean of 3.5 orders per minute. Let $ X $ represent the number of orders in 1 minute, and let $ Y $ represent the number of orders in 5 minutes. Given this claim, answer the following questions based on a mean of 3.5 orders per minute:a. Calculate $ P(X = 1) $, the probability of receiving exactly one order in a minute.b. Determine $ P(X \leq 1) $, the probability of receiving at most one order in a minute.(Note: There are no graphs or diagrams in this problem.)

Given information: The distribution is poisson distribution with parameters( m=3.5). Find:…

Answered: 6. A company's marketing department…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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6. Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poisson distribution, give the probability that strictly more than 5 customers arrive in a given hour. Translation: X has a Poisson distribution with mean 11. What is P (X > 5)?
Which random graph G(N, p) has (k) = 40 and variance o² of the degree distribution given by o² = 20?. Select one: O a. p= 1/2, N = 61 O b. p = 0.25, N = 161 O c. p = 2, N = 80 O d. None of the above.
Suppose that the following table records the average daily number of traffic accidents reported in the 20 areas of UK. Assuming that the occurrence of traffic accidents in the districts is random and follows the Poisson distribution, estimate the number of districts having various number of traffic accidents on a particular day and complete the table. Number of cases 0 1 2 3 4 >4 Observed number of area 1 4 6 5 2 0 Theoretical probability Estimated number of districts
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A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected and the amount of gas (therms) used during the month of January- is determined for each house. The resulting observations are 103, 156, 118,89,125,147,122,109,138,99. Let µ denote the average gas usage during January by all houses in this area. Compute a point estimate of µ. b.Suppose there are 10,000 houses in this area that use natural gas for heating. Let ℑ denote the total amount of gas used by all of these houses during January. Estimate ℑ using the data of part (a). What estimator did you use in computing your estimate? c. Use the data in part (a) to estimate p, the proportion of all houses that used at least 100 therms. d. Give a point estimate of the population median usage (the middle value in the population of all houses ) based on the sample of part (a).What estimator did you use?
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On average, there is one hurricane in the Bahamas every year. The cost torepair the damage of each hurricane in the Bahamas to a particular resort is 100. To stabilizefinances, the resort buys hurricane insurance, which will cover the cost of the repairs foreach hurricane after the second. Assume that the number of hurricanes in the Bahamas ina given year is Poisson distributed. 1. What is the expected cost of repairs in a given year to the resort (not including thecost of insurance)?2. What is the expected payout of the insurance company on the resort’s policy in agiven year?
Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.
A company's marketing department claims that the number of orders that are placed using theire-commerce store has a Poisson distribution with mean of 3.5 orders per minute. Let X be the number oforders in 1 minute. Let Y be the number of orders in 5 minutes. If the claim of a mean of 3.5 orders perminute is true a. What is P(Y = 15)? If the rate of orders falls to 2.1 per minute: b. What is P(X = 1)? c. What is the variance for X?

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