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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The number of people arriving per hour at the emergency room (ER) of a local hospital seeking medical attention can be modeled by the Poisson distribution, with a mean of 15 people per hour.The inter-arrival time, X, is defined as the time that passes between successive arrivals of patients seeking medical attention. (a) It has been 4 minutes since the last person seeking medical attention arrived at the ER. What is the probability that at least 9 minutes (in total) will pass until the next medical-attention-seeking person passes through the ER doors? Use four decimals in your answer.
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.
If a random variable follows a Poisson distribution and if: 4P(x=0)=P(x=1), then find E(x² ) Select one: o a. 0 o b. 30 OC. 20 od. 10
What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?
Example 24: Let X is a normal random variable denoted by N (0, ơ). Let Y =X°. Find the expected value of Y.
prob and stats
The lifetime (in years) of a washing machine from a particular company is an exponential random variable with parameter 1/5 . The company offers to replace any machine which breaks within 6 months. (a) What proportion of machines do they need to replace. (b) What is the expected time until a customer needs to buy a new machine? (Each time the company replaces a machine which breaks within 6 months, the company agrees to replace the new machine if it breaks within 6 months.)
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…
Given that is a random variable having a Poisson distribution, compute the following: (a) P(x = 8) when μ = 4 P(x) = (b) P(x 4) when μ = 3 P(x) = (d) P(x <8) when μ = 5.5 P(x) =
Elizabeth is a busy pediatrician. On any given day, she diagnoses an average of five babies with middle-ear infections. Assume that the number of babies who come to her clinic with middle-ear infections is a Poisson random variable. Calculate the probability that fewer than three babies with middle-ear infections will come to her clinic tomorrow. Give your answer in decimal form precise to three decimal places. P(X < 3) =

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