Homework Help is Here – Start Your Trial Now!
Math
Probability
(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?

(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?

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Question

#2 (please help with iv and v)

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?
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?
Expert Solution
steps

Step by step

Solved in 4 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS