Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers everyten minutes. The shop opens at 9am.(c) Let Y be the time (in hours) until the 4th customer arrives at the shop.State the distribution of Y and give the value(s) of its parameter(s).(d) Show that the probability of the time until the 4th customer arrives being greater than15 minutes is 13e-3.(e) Let M be the number of customers who arrive at the shop between 9am and 12 noon.State the distribution of M and give the value(s) of its parameter(s).(f) Calculate P(M = 30) using a normal approximation with the continuity correction.

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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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Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
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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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What do i specifically put in the box as p(x)=

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