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 person leaves with a random coats. Let us assume that all n! assignments of coats are equally likely. Let 0 ≤ l ≤ n be a fixed number. Find the probability that exactly l people out of n get their own coat back, and find the limit p(l) of this probability as n → ∞. The distribution on NU {0} given by p(l) is known as the Poisson distribution.

Q: A survey of 800 randomly selected adults in a certain country found that 82% believed that…

A: Solution-:Given: n=800, p=0.82 (or 82%)We want to verify the central limit theorem conditions.

Q: 10. Prove that (n) ≤ n/2 for n ≥ 8.

A: To prove that π(n) ≤ n/2 for n ≥ 8, where π(n) represents the number of prime numbers less than or…

Q: (a) Show that if n € N, then n+1 In dx. I

A:

Q: 9. Establish the Bernoulli inequality: If 1 + a > for all n ≥ 1. (1+a)" 0, then 1+ na

A:

Q: Show that for all x, e* > 1 +x.

A: It is given that, ex≥1+xwe have to show that for all x.

Q: 1 a) Sn+1 = 3 – Sn 25, -35m b) Sn+1 Sn-1 9Sn c) Sn+1 S+1

A:

Q: 7. Suppose A and B are compact subsets of R and that fn is a sequence of functions converging…

A:

Q: 3.4. 1. For a set A, let P be the set of all functions from A to the two-point set {0, 1}. Then |P|…

A: (1) Given: P is the set of all functions from A to the two-point set {0, 1}. Consider a map ß: P →…

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: Answer the following questions for the poset ([[1]. [2), (4), (1, 2), (1, 4), (2, 4), (3, 4), (1, 3,…

A:

Q: 21. Suppose (An) is a sequence of events. (a) If P (An) → 1 as n → ∞, prove there exists a…

A:

Q: Let A = {(−1)^n + 1/n where n is a positive integer}. Determine A′.(Recall that A′ is the set of…

A:

Q: 3. Suppose you roll a fair six-sided dice n times and X is their sum. Compute the central limit…

A: The provided information is as follows:A fair six-sided dice is rolled  times.The  is the sum of the…

Q: what is the limit as n goes to infinity of enn! divided by nn?

A: Since e^n &gt; n And rate of convergence (e^n × n!) &gt; rate of convergence (n^n)

Q: In a bag of 370 chocolate​ candies, 39 of them are brown. The candy company claims that 13​% of its…

A: Given : (i) 13% of all candies are brown (ii)Out of 370 candies in the bag, 39 are brown Step 1 :…

Q: 17. Find the limit of the following sequenc n² + 4n-4 4n2 +n-3 an %3D 0.25 a. b. 00 C. d. e. The…

A:

Q: Compute (a) E-ok · k! = (n+ 1)! – 1. (b) D (") = (). k=0 TIL

A: The problem can be solved using concepts of permutation and combination.

Q: Suppose that a patient receives an injection 9 mg of a certain drug and that 60% of the drug is…

A: It is given that The initial amount of drug intake=9 mg60% of the drug metabolize each day

Q: 8. Show that, at the n stage of the construction of the Cantor Middle- Thirds set, the sum of the…

A: Cantor Middle-thirds set: It is created by repeatedly deleting the open middle thirds of a set of a…

Q: Stickers. To celebrate the first day of spring, Lin is putting stickers on some of the 100 lockers…

A: Solution:-

Q: Sixty-seven percent of the U.S households, or about 85 million families, own a pet, according to the…

A: Given : p = 0.67 n = 800

Q: Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ²).…

A: Given equality: ∑i=0nxi·∑i=0nyi=∑i=0nxiyi   a) Verify the equality is always true. If not, give an…

Q: In a bag of 340 chocolate candies, 35 of them are brown. The candy company claims that 13% of its…

A: The question is about range rule of thumb.Given :Total number of chocolate candies ( n ) =…

Q: 5. Show that the following sequences of sets, {Ck }, are non-decreasing, (1.2.16), then find limg→∞…

A:

Q: A jar contains n red balls labeled from 1 to n where n ≥ 2 and m blue balls. a. Two balls are…

A: A jar contains n red balls labeled from 1 to n where  and m blue balls.Probability without…