You want to use a random graphG(N, p) with N 10³ to bestapproximate a Poisson random graphwith average degree (k) = 1/3.Which p would you prefer to use?Select one:O a.==р 0.33333O b. p = 0.03O c. p = 0.000333Od. p= 3 × 10-³

Given: Random graph, GN, p; N=103 Average degree, k=13To find: The preferred value of p.

Answered: You want to use a random graph G(N, p)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
You set up a series of cameras along the Mexican border. The rate of appearances of Jaguars is 4/18 years. Your cameras also produce pictures of wolf-sized canids, either wolves or coy-wolves in the same region. Each year your cameras catch about 400 of these animals, about 60 cougars and about 700 bears and 1200 feral hogs. Assume that these numbers are all population rates for Poisson. Given your cameras catch a non human large animal (and the above list is all of them): i. What is the probability it is a jaguar? (Hint: Animals are independent. This is asking the conditional probability of a jaguar, given you see an animal) ii. What is the probability it is a feral hog? iii. Out of 25 large nonhuman animals, what is the probability that 15 or more are feral hogs? (Hint N=25, P is fixed, independent trials) iv. Out of 180 large non human animals what is the probability that between 100 and 170 are feral hogs?
The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 7. (a) Compute the probability that more than 12 customers will arrive in a 2-hour period. (b) What is the mean number of arrivals during a 2-hour period.
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 X is a random variable of uniform distribution between 1 and 7. Find E(X)
Determine if the following scenarios follow a Poisson distribution or do not follow a Poisson Distribution. • You work in a shoe shop and you want to find the distribution of the total number of people who come into the store in a day. You also observe that there are usually more people who come into the shop over lunchtime (10-2 pm) and more people who come into the store after they finish work (5 pm-6 pm). Let X be the number of people who come into the shoe shop on a given day. No - not Poisson • You love peanut butter and want to know how many people buy peanut butter from Trader Joe's. One summer you have nothing to do so you go and stand in Trader Joe's every day and count how many people buy peanut butter in a given week. You assume that consumers do not impact each other's decisions. Let Y be the number of people who buy peanut butter in a given week. Yes - Poisson You want to know how many people in a group of 100 take painkillers if they have a headache. You think that the…
Q1: Suppose the number of customers X that enter a store between the hours 9:00 a.m. and 10:00 a.m. follows a Poisson distribution with parameter 0. Suppose a random sample of the number of customers that enter the store between 9:00 a.m. and 10:00 a.m. for 10 days results in the values 9, 7, 9, 15, 10, 13, 11, 7, 2, 12 Determine the maximum likelihood estimate of 0. Show that it is an unbiased estimator. Q2: Assume that X is a discrete random variable with pmf f(x). Let X₁,...,X₁ be a random sample on X. Suppose that the space of X is finite, say, D={a₁,...,m}. An intuitive estimate of p(a) is the relative frequency of a, in the sample. We express this more formally as follows. For j=1, 2,..., m, define the statistics 1,(X) = {1 0 X₁ = a; X₁ = a; Then the intuitive estimate of p(a)) can be expressed by the sample average p(a) = -1,(X₂) Find the unbiased estimator and the variance of the estimator and its mgf.
The graphs show a violation of the assumption of (check all that apply) normality homogeneity of variance

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You want to use a random graph G(N, p) with N = 10³ to best approximate a Poisson random graph with average degree (k) = 1/3.