Person P is walking with his dog every day. He decides to model the timeintervals between dog encounters (i.e., how long does it take between twoencounters) with the independent random variables Y1, . . ., Yn.Number of dogs encounters per day, the number of customers entering astore per hour, the number of bacteria per liter of water, etc. are classicallymodelled using the Poisson distribution. With an exponential distribution, onthe other hand, is used for modelling intervals of between events and howlong a light bulb lasts, for example. After learning this, person P decides tomodel the observations in such a way that the corresponding randomvariables Y1,..., Yn for a random sample, that is, independent observation, ofthe exponential distribution Exp(1/µ), µ > 0. The parameter μ > 0 is used asthe statistical model parameter 1 which is the expected value of eachobservation random variable Yi.Derive(a) the joint density function f(y;µ) specifying the model.(b) the likelihood function L(μ) and the log likelihood function I(p)

(a) Joint Density FunctionGiven that we have independent observations Y1,Y2,...,Yn from an…

Answered: Person P is walking with his dog every…

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 X and Y be two random variables. Suppose we know E(X) = 7 and E(Y)=3.Let Z = X − Y be a random variable. What is E(Z)? Justify your answer.
Which is not an assumed characteristic of & in the population model y₁ = Be + B₁ X₁ + εi? Multiple Choice It is a random variable. It has zero mean. ○ It is a statistic. It is unobservable.
prob and stats
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the height of a randomly selected male individual in a population is a normal random variable with mathematical expectation m=178 σ =8 what % of the individuals of this population is taller than 185cm?the height of the female individuals in this population is of normal distribution with parameters m=165 cm and σ=7cm. what % of the women are taller than half of the men
A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
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The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

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