Question

(Need solution for part b) You are offered to play the following game. You roll a fair 6-sided die once and observe the result which is shown by the random variable X. At this point, you can stop the game and win X dollars. Or, you can also choose to discard the X dollars you win in the first roll, and roll the die for a second time to observe the value Y . In this case, you will win Y dollars. Let W be the number of dollars that you win in this game.

b) If you have to pay the price of 1 dollar to do a second roll, i.e., you win Y − 1 dollars if you choose to roll the die a second time. Will you change your strategy? Why?

part a) was

What strategy do you use to maximize E[W]? What is the maximum E[W] you can achieve using your strategy?

Answer #1

You roll a fair 6-sided die once and observe the result which is
shown by the random variable X. At this point, you can stop and win
X dollars. Or, you can also choose to discard the X dollars you win
in the first roll, and roll the die for a second time to observe
the value Y. In this case, you will win Y dollars. Let W be the
number of dollars that you win in this game.
a)...

. A
dice game is played as follows: you pay one dollar to play, then
you roll a fair six-sided die. If you roll a six, you win three
dollars. Someone claims to have won a thousand dollars playing this
game nine thousand times. How unlikely is this? Find an upper bound
for the probability that a person playing this game will win at
least a thousand dollars.

In a game, you roll two fair dice and observe the uppermost face
on each of the die. Let X1 be the number on the first die and X2 be
the number of the second die. Let Y = X1 - X2 denote your winnings
in dollars.
a. Find the probability distribution for Y .
b. Find the expected value for Y .
c. Refer to (b). Based on this result, does this seem like a
game you should play?

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $12. If you roll a 2, 3, 4
or 5, you win $1. Otherwise, you pay $10.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest cent)
c....

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $9. If you roll a 2, 3, 4
or 5, you win $1. Otherwise, you pay $6
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest...

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $13. If you roll a 4 or 5,
you win $5. Otherwise, you pay $6.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ ____ (Round to the nearest
cent)
c. Interpret...

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $20. If you roll a 4 or 5,
you win $1. Otherwise, you pay $8.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest cent)
c. Interpret the...

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $7. If you roll a 4 or 5,
you win $1. Otherwise, you pay $8.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest cent)
c. Interpret the...

Suppose that you are offered the following "deal." You roll a
six sided die. If you roll a 6, you win $17. If you roll a 4 or 5,
you win $2. Otherwise, you pay $10.
a. Complete the PDF Table. List the X values, where X is the
profit, from smallest to largest. Round to 4 decimal places where
appropriate.
Probability Distribution Table
X
P(X)
b. Find the expected profit. $ (Round to the nearest cent)
c. Interpret the...

You play a gambling game with a friend in which you roll a die.
If a 1 or 2 comes up, you win $8. How much should you lose on any
other outcome in order to make this a fair game?

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