/Example 15-44. For the double Poisson distribution :p(x) = P(X = x) =1 em1.m;* 1 em2.m;*х!;x = 0, 1, 2, ...%3D%3D2°2х!show that the estimates for m, and m2 by the method of moments are : µi´±Vµ¿ – µí´ - Hi2.

Answered: Image /qna-images/answer/44dbd445-6a0a-4cd7-8e89-e480bdfa79ad.jpg

Answered: JExample 15-44. For the double Poisson…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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4.4. An individual picked at random from a population has a propensity to have accidents that is modelled by a random variable Y having the gamma distribution with shape parameter α and rate parameter β. Given Y = y, the number of accidents that the individual suffers in years 1, 2, . . . , n are independent random variables X1, X2, . . . Xn each having the Poisson distribution with parameter y. (a) Write down a function f so that the joint distribution of Y, X1, . . . , Xn can be described via P(a ≤ Y ≤ b, X1 = k1, X2 = k2 . . . Xn = kn) = Z b a f(y, k1, k2, . . . kn)dy and derive from this expression that, for your choice of f, Y has the Gamma distribution, and that conditionally on Y = y, X1, X2, . . . Xn are independent, each having the Poisson distribution with parameter y. (b) Find the conditional distribution of Y given that X1 = k1, X2 = k2, . . . , kn. (c) An insurance company has observed the number of accidents that an individual has suffered on each of n years and wishes to…
1. Let X be a Poisson random variable with E[X] = ln2. Calculate E[cosπX]. 2. The number of home runs in a baseball game is assumed to have a Poisson distribution with a mean of 3. As a promotion, Mall A pledges to donate 10,000 dollars to charity for each home run hit up to a maximum of 3. Find the expected amount that the company will donate. Mall B also X dollars for each home run over 3 hits during the game, and X is chosen so that the Mall B's expected donation is the same as the Mall A's. Find X.
If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded
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JExample 15-44. For the double Poisson distribution : p(x) = P(X = x) =! "1.m,* 1 e™2.m, x ! %3D x!;x= 0, 1,2, ... show that the estimates for m1 and m2 by the method of moments are : µ1´±Vµí - Hí - Hi'2.