A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
condition
Do, R₂
Do, R3
D1, R₂
D1, R3
P(Do) P(D₁)
.3
.7
Defended
Made
P(MoD, R) P(M₁|D, R)
.3
.7
.4
.6
.7
.3
.8
.2
Range
Points
condition
Mo, R₂
Mo, R3
M₁, R2
M1, R3
P(R₂) P(R3)
.6
.4
P(Po|M, R) P(P₂|M, R) P(P3|M, R)
1
0
0
1
0
0
0
1
0
0
1
Hint: For parts (a) and (b) below, using the definition of conditional probability and the fact of independence of
R 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 expected
value 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 expected
value 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 difference
represents.
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Transcribed Image Text:condition Do, R₂ Do, R3 D1, R₂ D1, R3 P(Do) P(D₁) .3 .7 Defended Made P(MoD, R) P(M₁|D, R) .3 .7 .4 .6 .7 .3 .8 .2 Range Points condition Mo, R₂ Mo, R3 M₁, R2 M1, R3 P(R₂) P(R3) .6 .4 P(Po|M, R) P(P₂|M, R) P(P3|M, R) 1 0 0 1 0 0 0 1 0 0 1 Hint: For parts (a) and (b) below, using the definition of conditional probability and the fact of independence of R 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 expected value 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 expected value 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 difference represents.
(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.
● 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).
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Transcribed Image Text:(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. ● 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).
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