Consider a random graph G(N, p) witheln 23Np==In the limit N → ∞ the average degree (k)is given by∞ 0 0 0 2/3 O None of the aboveTherefore the random graphhas 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…

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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Q6(a) Suppose X ~ x²(m), S = X+Y~x² (m+n), and X and Y are independent. Use moment-generating functions to show that S-X~x² (n). Q6(b) Let Y₁ ~ x² (n). The goal is to find the limiting distribution of Zn = (Yn-n) √2n as n → ∞. First, express the moment-generating function Mz, (t) of Zn in terms of the moment-generating function My, (t) of Yn. Then find ln(Mz, (t). Use the fact In(1-x) = -x-x² /2-x³/3 - ²/4 to show that as n →∞, Mz, (t) converges to et²/2 and hence Zn converges to N(0, 1) as n → ∞.
1
Consider a random graph G(N, p) with P = 2. -N² e N + 3N In the limit N→∞ the average degree (k) is given by O∞o Oo O2 ONone of the above Therefore the random graph Ohas not Ohas a giant component in the limit N →→ ∞.
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
Let X denote the length (in seconds) of the next smile of a ran- domly selected 8-week old baby. Suppose that X is uniformly distributed on the interval [0, 23]. (a) What is the probability that the next smile of a randomly selected 8-week old baby is between 15 and 25 seconds in length? (b) What is the moment generating function M(t) of X? No work is required for this part. 2.
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.)
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Consider a random graph G(N, p) with .In the limit N → ∞ the average degree (k) is given by 0 0 0 0 2/3 ○ None of the above Therefore the random graph O has not O has a giant component in the limit N → ∞. P = e² In 2 3N3/2
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Consider a random graph G(N, p) with eln 2 3N p= = In the limit N → ∞ the average degree (k) is given by ∞ 0 0 0 2/3 O None of the above Therefore the random graph has not O has a giant component in the limit N → ∞.