Find the following values by using the Poisson formulaP(X = 5|0= 2.3)P(X = 2|0= 3.9)3.а.%3D%3D%3DP(X < 3|0= 4.1)d. P(X = 0|0= 2.7)P(X = 1|0= 5.4)P(4

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Can balloons hold more air or more water before bursting? A student purchased a large bag of 12-inch balloons. He randomly selected 10 balloons from the bag and then randomly assigned half of them to be filled with air until bursting and the other half to be filled with water until bursting. He used devices to measure the amount of air and water was dispensed until the balloons burst. Here are the data
Compute the upper and lower limits for the following data at a 95% CI, when M1 = 20, M2 = 15, t = 2.145 (this is the t-value you would get from the table), and S(M1-M2) = 1.34.
The inhabitants of a city develop skin cancer at an approximate rate A. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: n ~ Poisson(X) X\n - Binomial(n, p) Question 5: What is the distribution of n X? n – X|X ~ Binomial X(1-p) 1- p We do not have enough information to answer this question. n|X Poisson(Xp) On - X|X ~ Poisson(A(1 – p) 1 for n > x n|X ~ fn|x (n|x) = n! 1- Di-o i! 0.w.
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a) Use the following table to find lower and upper estimates for ff(x)dx. X 3 4 67895 f(x) -3.4 -2.1 -0.6 0.3 0.9 1.4 1.8 48
Suppose that tax paid by a certain person per year is denoted T;, and is calculated using the following relationship to that persons gross income (G₁): Ti = 0.25(G₁ - 10000) (i.e, only people who have an income over $10,000 per year are taxed, and only the income beyond $10,000). You are told that the total gross income for an area with 200 people is $6,000,000. Assume that all the people measured make over $10,000 a year. (a) Find the total taxes collected for the 200 people. (b) Find ΣT; for the 200 people. 100 (c) Find (2G₁ – 40) for the 200 people.
The inhabitants of a city develop skin cancer at an approximate rate X. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: ~ U Poisson(A) X\n - Binomial(n, p) Question 4: What is the marginal distribution of X? Hint: two primary ways to do this: 1. you can summate out n from the joint distribution directly (more straightforward, but tricky algebra) o Pay attention to the lower limit of n o Remember that i=0 2. use MGFS + iterated expectation: E[etx] = En|Exn[etx n|| and then recognize the distribution corresponding to the MGF (need to understand MGFS and iterated expectation). o Obtain the inner expectation by using the Binomial theorem. O X Binoтial(n, Ap)…

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Find the following values by using the Poisson formula a. P(X = 5|0= 2.3) b. P(X = 2|0= 3.9) P(X < 3|0= 4.1) 3. %3D С.