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Transforms associated with uniform random variables. (a)

Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis ISBN: 9781886529236 227

Solution for problem 39 Chapter 4

Introduction to Probability, | 2nd Edition

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Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis

Introduction to Probability, | 2nd Edition

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Problem 39

Transforms associated with uniform random variables. (a) Find the transform associated with an integer-valued random variable X that is uniformly distributed in the range {a, a + 1, . . . , b}. (b) Find the transform associated with a continuous random variable X that is uniformly distributed in the range [a, bl . Solution. (a) The PMF of X is if k = a, a + 1. ... , b, otherwise. The transform is A1(s) = L esk p(X = k) k=-oc (b) We have b L - 1 sk e b-a + l k=a sa b-a _ e e sk b-a + l L..,. k=O e sa e s(b-a+l) - 1 b-a + l sx J b e Sx eS b - e sa M(s) = E[e 1 = a b _ a d x = s(b - a) .

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Simple Linear Regression  Analyzing relationship between 2 variables  X= hours studied Y=test score  Response variable (y)= dependent variable  Explanatory variable (x)= independent variable o Helper o Helps estimate mean of y’s  Scatterplot used to identify o Patterns/ relationships o Outliers  What regression line gives you o Line of means for y population o Prediction of the mean o Value of the regression equation is the “least squares” estimate of the mean of that y subpopulation  Include units!! sample correlation coefficient, r  Measures the strength of the LINEAR association between 2 quantitative variables  P= population corr

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Chapter 4, Problem 39 is Solved
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Textbook: Introduction to Probability,
Edition: 2
Author: Dimitri P. Bertsekas John N. Tsitsiklis
ISBN: 9781886529236

Introduction to Probability, was written by and is associated to the ISBN: 9781886529236. This full solution covers the following key subjects: . This expansive textbook survival guide covers 9 chapters, and 326 solutions. This textbook survival guide was created for the textbook: Introduction to Probability,, edition: 2. The answer to “Transforms associated with uniform random variables. (a) Find the transform associated with an integer-valued random variable X that is uniformly distributed in the range {a, a + 1, . . . , b}. (b) Find the transform associated with a continuous random variable X that is uniformly distributed in the range [a, bl . Solution. (a) The PMF of X is if k = a, a + 1. ... , b, otherwise. The transform is A1(s) = L esk p(X = k) k=-oc (b) We have b L - 1 sk e b-a + l k=a sa b-a _ e e sk b-a + l L..,. k=O e sa e s(b-a+l) - 1 b-a + l sx J b e Sx eS b - e sa M(s) = E[e 1 = a b _ a d x = s(b - a) .” is broken down into a number of easy to follow steps, and 142 words. The full step-by-step solution to problem: 39 from chapter: 4 was answered by , our top Statistics solution expert on 01/09/18, 07:43PM. Since the solution to 39 from 4 chapter was answered, more than 280 students have viewed the full step-by-step answer.

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