Question. Let S be the set of points contained in the circle of radius in R2, i.e. S = {(1,02) (x1, x₂) | x² + x² ≤ 1 √√π Let & be the collection of all Lebesgue measurable subsets of S (please don't worry too much about this). Let P(A) be defined as the area of A, for every subset A of S which is measurable (i.e. a member of E most subsets you can think of are measurable, so don't worry about this, it's just mentioned for completeness). Let (S, E, P) be the probability space we refer to, for this assignment problem. 1. Give examples of three non-empty independent events. 2. Give examples of three non-empty events that are pairwise indepen- dent but not independent. Please give explicit mathematical descriptions of all your events. For example, if your event is a square, you could describe it by specifying its vertices, or the vertices on a diagonal, etc. If your event is a circle, you should specify the coordinates of the centre and the radius.

Question. Let S be the set of points contained in the circle of radius in R2, i.e. S = {(1,02) (x1, x₂) | x² + x² ≤ 1 √√π Let & be the collection of all Lebesgue measurable subsets of S (please don't worry too much about this). Let P(A) be defined as the area of A, for every subset A of S which is measurable (i.e. a member of E most subsets you can think of are measurable, so don't worry about this, it's just mentioned for completeness). Let (S, E, P) be the probability space we refer to, for this assignment problem. 1. Give examples of three non-empty independent events. 2. Give examples of three non-empty events that are pairwise indepen- dent but not independent. Please give explicit mathematical descriptions of all your events. For example, if your event is a square, you could describe it by specifying its vertices, or the vertices on a diagonal, etc. If your event is a circle, you should specify the coordinates of the centre and the radius.

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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