Question

Suppose you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $6. Based on numerical values, should you take the deal? Explain your decision. Consider the following questions as you make your decision:

-What are you ultimately interested in here (the value of the roll or the money you win)?

-In words, define the random variable X.

- List the values that X may take on.

-Over the long run of playing this game, what are your expected average winnings per game?

Answer #1

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...

(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...

Conditional Expectation
You are offered the following game:
-A 6-faced fair die is rolled. Call the result of this roll
J
-A coin is flipped, if it lands heads you win 2^J dollars, if it
lands tails you win J.
a) What is the probability you win more than $25 at this
game?
b) Compute the conditional expectation conditional on J and then
use the Law of Iterated expectations to compute the expected value
of playing the game.
NOTE: this...

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)...

You roll a six-sided die repeatedly until you roll a one. Let X
be the random number of times you roll the dice. Find the following
expectation:
E[(1/2)^X]

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