atch against each other. This involves playing games of backgammon until one player has won four games, at which point that player is declared the winner of the match and no more games are played. Suppose that each player has a 50% chance of winning each game, and that this is independent of whoever wins the other games. Let G be a random variable with a value equal to the number of games that are played in the match. Let X be the event that Amy wins the first three games, let Y be the event that Amy wins the match and let Z be the event that G 7. (N.B. The result of the match can be recorded as a string of A's and B's of length G which indicates who won each game. For example, ABAAA would say that there were 5 games of which Ben only won the second one (so G = 5 and Amy won the match). Call this string the "score" for the match. You can write out all the possible scores, but there are a lot of them. It is better to classify and count scores without writing them all down. ] (i) Briefly explain (without any calculation), why Pr(Y) = . (ii) Find Pr(Z). (iii) Find Pr(Z|Y). (iv) Find Pr(Y|X). (v) Are X and Y independent events? (vi) Are Y and Z independent events? (vii) For g e {4, 5, 6, 7}, explain why Pr(G g) is equal to %3D 2(";") (). 9 - 1 (viii) Use the formula from part (vii) to find E[G].
atch against each other. This involves playing games of backgammon until one player has won four games, at which point that player is declared the winner of the match and no more games are played. Suppose that each player has a 50% chance of winning each game, and that this is independent of whoever wins the other games. Let G be a random variable with a value equal to the number of games that are played in the match. Let X be the event that Amy wins the first three games, let Y be the event that Amy wins the match and let Z be the event that G 7. (N.B. The result of the match can be recorded as a string of A's and B's of length G which indicates who won each game. For example, ABAAA would say that there were 5 games of which Ben only won the second one (so G = 5 and Amy won the match). Call this string the "score" for the match. You can write out all the possible scores, but there are a lot of them. It is better to classify and count scores without writing them all down. ] (i) Briefly explain (without any calculation), why Pr(Y) = . (ii) Find Pr(Z). (iii) Find Pr(Z|Y). (iv) Find Pr(Y|X). (v) Are X and Y independent events? (vi) Are Y and Z independent events? (vii) For g e {4, 5, 6, 7}, explain why Pr(G g) is equal to %3D 2(";") (). 9 - 1 (viii) Use the formula from part (vii) to find E[G].
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question statement is lengthy but I believe answers are quite simple. Please do it perfectly :)
![Amy and Ben agree to play a "best of 7" backgammon match against each other. This involves
playing games of backgammon until one player has won four games, at which point that player
is declared the winner of the match and no more games are played. Suppose that each player
has a 50% chance of winning each game, and that this is independent of whoever wins the other
games. Let G be a random variable with a value equal to the number of games that are played
in the match. Let X be the event that Amy wins the first three games, let Y be the event that
Amy wins the match and let Z be the event that G 7.
[N.B. The result of the match can be recorded as a string of A's and B's of length G which indicates
who won each game. For example, ABAAA would say that there were 5 games of which Ben only
won the second one (so G = 5 and Amy won the match). Call this string the "score" for the match.
You can write out all the possible scores, but there are a lot of them. It is better to classify and count
scores without writing them all down. ]
(i) Briefly explain (without any calculation), why Pr(Y) = .
(ii) Find Pr(Z).
(iii) Find Pr(Z |Y).
(iv) Find Pr(Y |X).
(v) Are X and Y independent events?
(vi) Are Y and Z independent events?
(vii) For g e {4, 5, 6, 7}, explain why Pr(G g) is equal to
1
(viii) Use the formula from part (vii) to find E[G].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75d7a01c-c361-41f3-b8b8-16ef30a9714c%2Fb10f0606-d3cc-4fe7-8dea-95a1c5e1e79f%2F6zm5z3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Amy and Ben agree to play a "best of 7" backgammon match against each other. This involves
playing games of backgammon until one player has won four games, at which point that player
is declared the winner of the match and no more games are played. Suppose that each player
has a 50% chance of winning each game, and that this is independent of whoever wins the other
games. Let G be a random variable with a value equal to the number of games that are played
in the match. Let X be the event that Amy wins the first three games, let Y be the event that
Amy wins the match and let Z be the event that G 7.
[N.B. The result of the match can be recorded as a string of A's and B's of length G which indicates
who won each game. For example, ABAAA would say that there were 5 games of which Ben only
won the second one (so G = 5 and Amy won the match). Call this string the "score" for the match.
You can write out all the possible scores, but there are a lot of them. It is better to classify and count
scores without writing them all down. ]
(i) Briefly explain (without any calculation), why Pr(Y) = .
(ii) Find Pr(Z).
(iii) Find Pr(Z |Y).
(iv) Find Pr(Y |X).
(v) Are X and Y independent events?
(vi) Are Y and Z independent events?
(vii) For g e {4, 5, 6, 7}, explain why Pr(G g) is equal to
1
(viii) Use the formula from part (vii) to find E[G].
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