Engineers observe that about 90% of graphite samplesfracture within 5 hours when subjected to a certain stress.(a) If the time to fracture is modeled with an exponentialdistribution, what would be a suitable value for theparameter λ?(b) Use the model to estimate the probability that afracture occurs within 3 hours.

The exponential distribution is often used to model the time between events in a Poisson process. It…

Answered: Engineers observe that about 90% of…

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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In this example, what is the probability of a person who lives in a single home with a single family with multiple generations getting infected with Covid? Enter the answer to three digits after the decimal place.
Use the information below to answer Questions #16 - 22. The article "Probabilistic Fatigue Evaluation of Riveted Railway Bridges" (J. of Bridge Engr., 2008: 237- 244) suggested the exponential distribution with A = 9 as a model for the distribution of stress range (MPa) in certain bridge connections. What proportion of stress ranges are at least 2 MPa? Round to four decimal places as needed.
The type of battery in Jim's laptop has a lifetime X (in years) which follows a Weibull distribution with parameters α=2 and β=4. The type of battery in Jim's tablet has a lifetime Y (in years) which follows an exponential distribution with parameter λ=1/4.Find E(XY−2Y).(Answer as a decimal number, and round to 2 decimal places).
A quality control team studies the relationshipbetween years of experience (x) for individualdesign employees and ability to complete acomplex project within a certain time frame (y),where Y = 1 if the project is successfullycompleted, and Y = 0 if not. We know: b0 = −1.68and b1 = 0.12.a) Write the estimated logit function.b) Estimate the odds that a design employeewith 10 years of experience completes thecomplex project.c) Find and interpret the estimated odds ratiofor this model.
Can gender, educational level, and age predict the odds that someone votes for a particular candidate in the election? Over 1500 voters were selected, and data were col-lected on the highest year of school completed, their age, and their gender. We wish to t a logistic regression model: log(1 p p ) = 0 + 1Age + 2Education + 3Gender, where p is the binomial probability that a person voted for candidate Johnson, and gender is coded as the indicator for female. The R output is given below. parameter df estimate s.e z p-value (Intercept) 1 .1119 .3481 .321 .748 Age 1 .0020 .0032 .613 .54 Education 1 -.0100 .0184 .547 .585 Gender 1 .4282 .1040 4.117 .000 Null deviance: 255.95 on 1499 degrees of freedom Residual deviance: 220.80 on 1496 degrees of freedom Write down the tted logistic regression and give a short summary about the data analysis . Calculate the probability of voting for Johnson for a…
Suppose you obtain the following regression model, E[y]=91+79*x1 +20*x1*x2. What is the impact of a 39 unit change of x1 on the expected value of y when x2 is at its mean of 40?
A individual, with a utility function lnW and an initial wealth level W0, is faced with a fair gamble of winning or losing $h (where W0 > h > 0) with 50-50 chance. (a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such a gamble. Give the equation that determines f, and solve the equation for f (i.e., express f in terms of W0 and h). (c) Show that f increases as h increases.
You are planning to go fishing with two friends. The time (in hours) before you catch a fish is exponentially distributed with parameter 6. How long do you need to arrange for the fishing so that there is a 95% probability that everyone catches at least one fish? [Assume that the events that each person catches a fish are independent.]

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