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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Refer to the coin-tossing game in Exercise 3.2. Calculate

Chapter 3, Problem 13E

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QUESTION:

Problem 13E

Refer to the coin-tossing game in Exercise 3.2. Calculate the mean and variance of Y, your winnings on a single play of the game. Note that E(Y) > 0. How much should you pay to play this game if your net winnings, the difference between the payoff and cost of playing, are to have mean 0?

Reference

You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $1; if the faces are both heads, you win $2; if the coins do not match (one shows a head, the other a tail), you lose $1 (win (−$1)). Give the probability distribution for your winnings, Y , on a single play of this game.

Questions & Answers

QUESTION:

Problem 13E

Refer to the coin-tossing game in Exercise 3.2. Calculate the mean and variance of Y, your winnings on a single play of the game. Note that E(Y) > 0. How much should you pay to play this game if your net winnings, the difference between the payoff and cost of playing, are to have mean 0?

Reference

You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $1; if the faces are both heads, you win $2; if the coins do not match (one shows a head, the other a tail), you lose $1 (win (−$1)). Give the probability distribution for your winnings, Y , on a single play of this game.

ANSWER:

Solution :

Step 1 of 1:

Given the upper faces on the coins are both tails, you win $1 and

The both faces are heads, you win $2.

Here one is a head and another one is tail, you lose $1 or win -$1.

So, tails-tails = $1, heads-heads=$2, heads-tails=-$1, tails-heads$1.

Our goal is:

We need to find calculate the mean and the variance of Y and

We have to find the how much should you pay to play if your net winning, the difference between the payoff and the cost of playing, are to have mean 0.

Now we have to calculate the mean and the variance of Y.

First we have to calculate the mean.

The mean of Y is

=E(Y)=(-1)+(1)+(2)

            =++

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