A mechatronic assembly is subjected to a final functional test. Suppose that defects occur at random in theseassemblies, and that defects occur according to a Poisson distribution with parameter >= 0.02.(a) What is the probability that an assembly will have exactly one defect?(b) What is the probability that an assembly will have one or more defects?(c) Suppose that you improve the process so that the occurrence rate of defects is cut in half to λ = 0.01.What effect does this have on the probability that an assembly will have one or more defects?

Step 1:Probability mass function of poisson distribution P(X=x)=x!e−λλx whereX = number of…

Answered: A mechatronic assembly is subjected to…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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(a) The number of reported traffic accidents at a dangerous crossroads each month is believed to follow a Poisson distribution, Poi(µ). Seven accidents occur during a particular month. Estimate µ, giving approximate error bounds (± 2 × standard error). (b) Suppose that the actual value of µ is 4 accidents/month. Find (i) the probability of obtaining a value as large as, or larger than 7 on any given month. (ii) the mean and variance of the total number of accidents likely to be reported during a full year.
7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determines the number of missing/corrupted packets. Suppose that number X has a Poisson distribution with parameter 23. = (a) What is the probability that the counter determines that the transmission has exactly one miss- ing/corrupted packet of data? (b) What is the probability that the counter determines that the transmission has at least 3 miss ing/corrupted packets of data? (c) If two transmissions of data across the internet ar that at least one of them does not contain a missing/corrupted packet? e independently selected, what is the probability
Suppose that earthquakes occur according to a Poisson process with rate λ = 0.2 per day. (a) What is the probability that there will be 2 or fewer earthquakes in April? (b) Starting from now, what is the probability that the second earthquake will occur within a week?
The probabilities of various numbers of failures in a mechanical test are as follows: Pr[0 failures] = 0.21, Pr[l failure] = 0.43, Pr[2 failures] = 0.28, Pr[3 failures] = 0.08, Pr[more than 3 failures] = 0. (a)Show this probability function as a graph with number of failures in x-axis and probability in y-axis. (b)Sketch a graph of the corresponding cumulative distribution function. Hint: cumulative probability in y-axis (c)What is the expected number of failures, E, or the mathematical expectation of the number of failures?
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1 β e−x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = e−a/β − e−b/β Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. μ = β and σ = β Note: The number e = 2.71828 is used throughout…
If the number X of particles emitted during a 1-h period from a radioactive source has a Poisson distribution with parameter 2 = 4 and that the probability that any emitted particle is recorded is p = 0.9, find the probability distribution of the number Y of the particles recorded in a 1-h period and hence the probability that no particle is recorded.
If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded
Suppose a radioactive source is metered for 3 hours, during which time the total number of alpha particles counted is 328. Modeling the problem using a Poisson distribution, what is the probability exactly four particles will be counted in the next 2 minutes? Answer the question in two ways: (a) By defining X to be the number of particles counted in 2 minutes (b) By defining X to be the number of particles counted in 1 minute. Give your answers in decimal form with at least 6 significant figures.
An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poissonrandom variable with λ = 7.5. (a) What is the probability that at most 5 cars per year will experience a catastrophe?(b) What is the probability that more than 1 car per year will experience a catastrophe?
max (a) A structure consists of 100 column footings. Suppose the settlement of each footing is exponentially distributed with a mean of 2 inches and the settlements between footings are statistically independent. What is the probability that the maximum settlement S among the 100 footings will not exceed 5.0 inches? Compare this exact probability with the answer obtained assuming an appropriate asymptotic distribution for S. (b) What is the probability that the minimum settlement Sis at least 0.5 inch? (c) Determine the mean and coefficient of variation of the maximum differential settlement A defined as (S-Smin). min max
Genetic Creutzfeldt-Jakob Disease (gCJD) is a very rare disease, and the number of deaths caused by gCJD each year in the United Kingdom can be modeled using a Poisson distribution with unknown parameter 0. Numbers of gCJD deaths for the period 2005-9 are given in Table 12. A Gamma(11, 2) was selected as a prior for 0. Year Number of deaths Table 12 2005 2006 13 9 2007 2008 2009 9 5 8 (a) State the posterior for parameter 0, given the data and prior above. (b) Calculate the posterior mode for 8, giving your answer to 2 decimal places. (c) Figure 11 shows the prior, likelihood and posterior for 8. Figure 11 10 Prior Likelihood Posterior 15 Comment on the relative contributions of the prior and data to the posterior, justifying your opinion. How have the data affected opinion about ?
Define the Distributed Lag Model with Additional Lags and AR(p) Errors?

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