Exercise 3.44. Choose a point uniformly at random in that half of the unit disk that is to the right of the y-axis. In other words, choose a point uniformly at random from the set {(x,y) : x > 0,x2 +y2 < 1}. Let S be the slope of the line through the chosen point and the origin. (a) Find the cumulative distribution function of S. (b) Find the probability density function of S.

Exercise 3.44. Choose a point uniformly at random in that half of the unit disk that is to the right of the y-axis. In other words, choose a point uniformly at random from the set {(x,y) : x > 0,x2 +y2 < 1}. Let S be the slope of the line through the chosen point and the origin. (a) Find the cumulative distribution function of S. (b) Find the probability density function of S.

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Description: Exercise 3.44. Choose a point uniformly at random in that half of the unit disk that is to the right of the y-axis. In other words, choose a point uniformly at random from the set {(x,y) : x > 0,x2 +y2 < 1}. Let S be the slope of the line through the

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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Exercise 3.44. Choose a point uniformly at random in that half of the unit disk that is to the right of the y-axis. In other words, choose a point uniformly at random from the set {(x,y) : x > 0,x2 +y2 < 1}. Let S be the slope of the line through the chosen point and the origin. (a) Find the cumulative distribution function of S. (b) Find the probability density function of S.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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