to achieve ten points is to receive a pot of 100 francs. The game is interrupted at the point where outcome of a coin toss. Fermat bets on heads (H) and Pascal bets on tails (T). The first of the two players 2. In lecture 12, we studied the Problem of Points. A point is given to whoever bets correctly on the to achieve ten points is to receive a pot of 100 francs. me game is interrupted at the point where Fermat is winning 8 points to 7 points. How is the 100-iranc pot to be divided? To answer this, we need to find what the chance would be for each of them to win the game if it were finished. Since Fermat needed only two more points to win tne game, and Pascal needed three, the game would have been over after four more tosses of the coin. Tne sample space of tossing a coin four times is HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHHTTHT TTTH TTT (i). Suppose the coin is fair. The outcomes are equally likely. Define random variable X as the count of heads. What is the probability distribution of X? bebsini (ii). Find the mean and the standard deviation of X. (iii). Suppose in a different universe the coin is not fair, say the probability of getting a head is 0.4. Define random variable Y as the count of heads. What is the probability distribution of Y? (iv). Are X and Y binomial random variables? If yes, use formulas for binomial distributions to check your results in (i) and (ii). (v). Now the game ends when someone achieves eleven points. Fermat is winning 8 points to 7 points when the game is interrupted. Suppose the coin is fair. How is the 100-franc pot to be divided?
to achieve ten points is to receive a pot of 100 francs. The game is interrupted at the point where outcome of a coin toss. Fermat bets on heads (H) and Pascal bets on tails (T). The first of the two players 2. In lecture 12, we studied the Problem of Points. A point is given to whoever bets correctly on the to achieve ten points is to receive a pot of 100 francs. me game is interrupted at the point where Fermat is winning 8 points to 7 points. How is the 100-iranc pot to be divided? To answer this, we need to find what the chance would be for each of them to win the game if it were finished. Since Fermat needed only two more points to win tne game, and Pascal needed three, the game would have been over after four more tosses of the coin. Tne sample space of tossing a coin four times is HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHHTTHT TTTH TTT (i). Suppose the coin is fair. The outcomes are equally likely. Define random variable X as the count of heads. What is the probability distribution of X? bebsini (ii). Find the mean and the standard deviation of X. (iii). Suppose in a different universe the coin is not fair, say the probability of getting a head is 0.4. Define random variable Y as the count of heads. What is the probability distribution of Y? (iv). Are X and Y binomial random variables? If yes, use formulas for binomial distributions to check your results in (i) and (ii). (v). Now the game ends when someone achieves eleven points. Fermat is winning 8 points to 7 points when the game is interrupted. Suppose the coin is fair. How is the 100-franc pot to be divided?
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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#2 (please help with i, ii, and iii)
Transcribed Image Text:to achieve ten points is to receive a pot of 100 francs. The game is interrupted at the point where
outcome of a coin toss. Fermat bets on heads (H) and Pascal bets on tails (T). The first of the two players
2. In lecture 12, we studied the Problem of Points. A point is given to whoever bets correctly on the
to achieve ten points is to receive a pot of 100 francs. me game is interrupted at the point where
Fermat is winning 8 points to 7 points. How is the 100-iranc pot to be divided? To answer this, we need
to find what the chance would be for each of them to win the game if it were finished.
Since Fermat needed only two more points to win tne game, and Pascal needed three, the game would
have been over after four more tosses of the coin. Tne sample space of tossing a coin four times is
HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHHTTHT TTTH TTT
(i). Suppose the coin is fair. The outcomes are equally likely. Define random variable X as the count of
heads. What is the probability distribution of X?
bebsini
(ii). Find the mean and the standard deviation of X.
(iii). Suppose in a different universe the coin is not fair, say the probability of getting a head is 0.4.
Define random variable Y as the count of heads. What is the probability distribution of Y?
(iv). Are X and Y binomial random variables? If yes, use formulas for binomial distributions to check your
results in (i) and (ii).
(v). Now the game ends when someone achieves eleven points. Fermat is winning 8 points to 7 points
when the game is interrupted. Suppose the coin is fair. How is the 100-franc pot to be divided?
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