Consider a random graph G(N, p) withe² In 23N 3/2р=.In the limit N → ∞ the average degree (k)is given by∞ 0O O O 2/3 O None of the aboveTherefore the random graphO has not O hasa giant component in the limit N → ∞.

The objective of the question is to determine the average degree (k) of a random graph G(N, p) in…

Answered: Consider a random graph G(N, p) with e²…

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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3. Let Z~ Normal(0, 1), and let Q(1) = Pr[Z > 1]. (There is no closed form for Q(1), but it is approximately 0.159.) Find the conditional expectation E[Z | Z > 1] in terms of Q(1).
Suppose that X1,..., Xn are i.i.d. Poisson(0) where 0 > 0 is an unknown parameter. The prior T(0) on 0 is assumed to be Gamma(a, 8). Find the Bayesian estimator with respect to the loss function L(0, a) = (0 – a)?. B(a + s) n+ B Ôbayes s(n + a) Ôbayes (B + 8)(n + a) (B + a)(n + s) Ôbayes (a + s)(n + B)
A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (For now, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/λ, where λ is a positive parameter. Let the unit of time be an hour. Question 11 What's E{N₁ N₂} in terms of X ? 4λ² + A 21/12 1² 21² +1 21² Question 12 Let 7; be the i th inter-arrival time. Which of the following statements is true? P(T1+T2 + T3 > 2) = P(N₂ ≤ 2) P(71 > 1) = P(N₁ = 1) P(T1+T2 + T3 > 2) = P(N₂ ≤ 3)
O. I only need question 2 solved! It involves discrete math!
2
q6, a and b please
(8) Discuss but no need to submit. Let g = Σx_ n=1 many terms will you use? (−1)n n² Approximate g to within 0.01. How
A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (For now, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/λ, where A is a positive parameter. Let the unit of time be an hour. Question 8 What is E{N₁} ? (In N₁ the sub index 1 is a time (one hour).) 1 1² 1 1 Question 9 Are the r.v.'s N₁ and N₂ independent? (The sub index 2 in N₂ is a time (two hours).) Yes No Question 10 Are the r.v.'s N₁ and N₂ – N₁ dependent? Yes No
Q1. A continuous r.v. X is said to have a N (u,o) distribution if it's moment generating function (m.g.f.) is given by Mx (t) =e Let X1.X2,...X „ be a random sample of size n from a 2 N (4,02) distribution and Let Y = X, and X %3D i =1 (a) Find the m.g.f. My (t) of Y. (b) State the distribution of Y specifying the parameters. (c) Find the m.g.f. M x) of X .
4
Consider a Poisson process of intensity λ > 0 events per hour. Suppose that exactly one event occurs in the first hour. Let X be the time at which this event occurs, measured in hours (so that the possible values of X are the reals in the interval [0, 1]). (a) What is P (0 ≤ X ≤ a) for a ∈ [0, 1]? (Of course, we are conditioning on exactly one event occurring in the first hour, as described.) Hint: Consider the number of events that occur in [0, a] and in (a, 1], similar to question #5 on the previous homework. (b) What is the distribution of X, under the same conditions? (You might want to wait until Monday’s class after break to do this last part.)
9.

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Consider a random graph G(N, p) with e² In 2 3N 3/2 р = .In the limit N → ∞ the average degree (k) is given by ∞ 0 O O O 2/3 O None of the above Therefore the random graph O has not O has a giant component in the limit N → ∞.