Suppose n people arrive for a show and leave their coats in the cloakroom. Unfor-tunately, the cloakroom attendant mixes up the coats completely so that each personleaves with a random coats. Let us assume that all n! assignments of coats are equallylikely. Let 0 ≤ l ≤ n be a fixed number. Find the probability that exactly ¤ people outof n get their own coat back, and find the limit p(l) of this probability as n → ∞. Thedistribution on NU {0} given by p(l) is known as the Poisson distribution.

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Answered: Suppose n people arrive for a show and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Sixty-seven percent of the U.S households, or about 85 million families, own a pet, according to the 2019-2020 national pet owners survey conducted by the American pet products association (APPA). A small pet shop opens in your neighborhood and randomly and independently select 800 families to attend the grand opening of the store. Check the conditions of the central limit theorem for this scenario. What is the size of the population?
According to a survey, 55% of young Americans aged 18 to 29 say the primary way they watch television is through streaming services on the Internet. Suppose a random sample of 400 Americans from this age group is selected. Complete parts (a) through (d) below. Question content area bottom Part 1 a. What percentage of the sample would we expect to watch television primarily through streaming services? enter your response here% Part 2 b. Verify that the conditions for the Central Limit Theorem are met. The Random and Independent condition ▼ holds assuming independence. holds through an exception. does not hold. The Large Samples condition ▼ does not hold. holds. The Big Populations condition ▼ can cannot reasonably be assumed to hold. Part 3 c. Would it be surprising to find that 227 people in the sample watched television primarily through streaming services? Why or why not? Select the correct choice below and fill in the answer box…
In an area having sandy soil, 60 small trees of a certain type were planted, and another survive 1 year and Y= the number of trees planted in clay soil that survive 1 year. If the probability in clay soil is 0.6, compute an approximation to P(-6 ≤X-Y≤ 6) (do not bother with the continuity LUSE SALT 60 trees were planted in an area that a tree planted correction). (Round having in sandy clay soil will survive 1 year is 0.7 and the probability your answer to four decimal places.) soil. Let X = the number of trees planted in sandy of 1-year soil that survival
Suppose poset (A, R), where A = {1, 2, 3, 4, 6, 8. 9. 12, 16, 18, 32, 36} and the relation R runs outdivide. Answer the following questions:a. Draw a Hasse Diagram for the poset (A, R)b. Find the upper limit of {6, 9}c. Supremum of {6, 9}
5. Show that the following sequences of sets, {Ck }, are non-decreasing, (1.2.16), then find limä-∞ Ck- Ck = {x : 1/k < x < 3 – 1/k}, k = 1, 2, 3, ....
In which case do you need to use the Central Limit Theorem? When X is normal and n is any number When X is not normal and n is any number When X is not normal and n> 30 When X is normal and n > 30
According to data released in 2016, 69% of students in the United States enroll in college directly after high school graduation. Suppose a sample of 150 recent high school graduates is randomly selected. After verifying the conditions for the Central Limit Theorem are met, find the probability that at most 66% enrolled in college directly after high school graduation. First, verify that the conditions of the Central Limit Theorem are met. The Random and Independent condition holds assuming independence. The Large Samples condition holds. The Big Populations condition can reasonably be assumed to hold. The probability is. (Type an integer or decimal rounded to three decimal places as needed.)
A discrete source has 8 symbols x-[x1, x2, x3, x4, x5, x6, x7, x8] with probability P- [1/4, 1/4, 1/8, 1/8, 1/16, 1/16, 1/16, 1/16]. Find info content in each symbol then calculate the entropy.
A researcher records the number of employees of each of the IT companies in a certain town. The results are summarized in the table. Find the class limits of the third class. Number of Employees Number of IT Companies 0-799 38 800 - 1,599 24 1,600 - 2,399 6 2,400 - 3,199 7 3,200 - 3,999 O A. lower limit = 1,600; upper limit = 2,400 B. lower limit = 1,599; upper limit = 2,400 O C. lower limit = 1,600; upper limit = 2,399 D. lower limit = 1,599.5; upper limit = 2,399.5
A circle is said to minimize a set of points if it is a circle with minimal radius such that all the points in the set are inside or on it. 12 points are equally spaced on circle w. A set of 4 out of these 12 points is chosen at random. Find the probability that w minimizes this set. (A) (B) (C) 19 (D) (E) 1

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