In Exercise 5.3, we determined that the joint probability distribution of Y1, the number ofmarried executives, and Y2, the number of never-married executives, is given byOO.()33 — У1 — У2P(y1, y2) :where y, and y2 are integers, 0 < yı < 3,0 < y2 < 3, and 1 < y1 + y2< 3.a Find the marginal probability distribution of Y1, the number of married executives amongthe three selected for promotion.b Find P(Y1 = 1|Y2 = 2).c If we let Y3 denote the number of divorced executives among the three selected for promo-tion, then Y3 = 3 – Y1 – Y2. Find P(Y3 = 1|Y2 = 1).

a)The joint probability distribution of Y1 , the number of married executives and Y2, the number of…

Answered: In Exercise 5.3, we determined that the…

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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Let Y be an exponential random variable with (unknown) mean 0.
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Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y₁, . . ., Yn . Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter µ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. (a) Form the maximum likelihood estimate μ^(y) in the model for the parameter μ…
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Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
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