conditionDo, R₂Do, R3D1, R₂D1, R3P(Do) P(D₁).3.7DefendedMadeP(MoD, R) P(M₁|D, R).3.7.4.6.7.3.8.2RangePointsconditionMo, R₂Mo, R3M₁, R2M1, R3P(R₂) P(R3).6.4P(Po|M, R) P(P₂|M, R) P(P3|M, R)10010001001Hint: For parts (a) and (b) below, using the definition of conditional probability and the fact of independence ofR and D, we can know that: P(M₁, Rj|Dk) = P(Mi|Dk, Rj)P(Rj).(a) Compute P(M, R|D₁) for all possible values of M and R; that is, find:• P(Mo, R₂|D₁)• P(Mo, R3|D1)• P(M₁, R₂|D1)• P(M₁, R3|D1)(b) Compute P(M, R|Do) for all possible values of M and R; that is, find:• P(Mo, R₂|Do)• P(Mo, R3|Do)• P(M₁, R₂|Do)• P(M₁, R3|Do)(c) Using part (a), give the distribution of points earned given a shot is defended and compute the expectedvalue of points earned when a shot is defended.(d) Using part (b), give the distribution of points earned given a shot is not defended and compute the expectedvalue of points earned when a shot is not defended.(e) Using parts (c) and (d), compute the difference in expected points earned between defended and unde-fended shots. Write one sentence, easily understood by a non-technical reader, which explains what this differencerepresents. (6) At the top of the next page is a Bayes Net graph and four tables which characterize how four random variablesinteract to describe a single basketball shot:• D (defended): whether the player taking the shot was defended (D₁) or not (Do) while taking the shot.● R (range): whether the player took a 2-point shot (R₂) or a 3-point shot (R3).● M (made): whether the shot was made (M₁) or not (Mo).● P (points): the points earned as a result of the shot, either 0 (Po), 2 (P₂), or 3 (P3).

Answered: (6) At the top of the next page is a…

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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(6) At the top of the next page is a Bayes Net graph and four tables which characterize how four random variables interact to describe a single basketball shot: • D (defended): whether the player taking the shot was defended (D₁) or not (Do) while taking the shot.