5 18). Starting at 9: 00am, assengers arrive at a train station as a Poisson process withrate A = 2 per minute. The next train will depart at time T, where T is uniformlydistributed between 9: 10am and 9: 15am. Compute the mean waiting time for apassenger at the station before the train departs. [Hint: condition on T and N(T),the number of passengers who depart on the train]. IAnswer: 6 mins 15 sec.

Answered: Image /qna-images/answer/3694f10c-b823-479a-a9ca-e8c4b98e355a.jpg

Answered: 18). Starting at 9: 00am, assengers…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that the variables Y1, Y2,... in a compound Poisson process have Bernoulli distribution with parameter p . Show that the process reduces to the Poisson process of parameter λp.
Let {N_1(t)} and {N_2(t)} be two independent Poisson processes with rates λ1=1 and λ2=2, respectively. Find the probability that the second arrival in N_1(t) occurs before the third arrival in N_2(t). Round answer to 4 decimals.
A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.b. Compute A and B Use the Poisson approximation for your calculations
Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?
Let X1,...Xn be iid Poisson(λ1) and Y1,...,Ym be iid Poisson(λ2). Write out the GLRT for testing H0: λ1 = λ2 versus Ha: λ1 ≠ λ2.
Let X1, X2, ... , Xn be a random sample from N(μ, σ2). Find the Moment Generating Function of X̅. If n = 16 and σ = 2, compute P(-1 ≤ X̅ - μ ≤ 1).
Assume that N(t) is a Poisson process with rate λ=2024. ComputeP(N(s) =1000,N(t) =2023),for any s≤t
In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Poisson distribution with probability mass function f(x), where f(x) = θ x e −θ/x! and θ is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats, it was.
In a video game with a time slot of fixed length T, signals are generated according to a Poisson process with rate λ, where T > 1/λ. During the time slot you can push a button only once. You win if at least one signal occurs in the time slot and you push the button at the occurrence of the last signal. Your strategy is to let pass a fixed time s with 0 < s < T and push the button upon the first occurrence of a signal (if any) after time s. What is your probability of winning the game? What value of s maximizes this probability?
Define the random process {Xt} by Xt = et + θ et−1. Show this process is weakly stationary.
2a) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Find lambda λ? 2b) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Using Normal approximation, we will need to find the probability that the Sarah’s garden will contain less than 45 flowers. First graph and answer what is the continuity correction? 2c) Using the previous results for lambda and continuity correction, find z, then graph and use your table to find φ table value of z Write down your final answer for the probability that Sarah’s garden will contain less than 45 flowers as a decimal number with 4 decimal places.
Given is the number of calls arriving at a telephone exchange by a Poisson process with the intensity λ= 5 calls per 10 minutes. The following question I have to compute: 1. Compute the probability that at least one call will arrive in the next twominutes. 2. Find the probability that either A [ no calls arrive in the next two minutes ] or B [ exactly two calls arrive in the next four minutes ] 3. Let X denote the number of calls arriving in two minutes and Y = X + 1. Compute E(Y2).

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