Question

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?

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)...

Consider the experiment of tossing 2 fair dice independently and
let X denote their difference (first die minus second die).
(a) what is the range of X?
(b) find probability that X=-1.
(c) find the expected value and variance of X. Hint: let X1,
X2 denote #s on the two dice and write X=X1-X2

Consider the following game. You roll two fair dice. If you roll
a sum of 8, you win $9. Otherwise, you lose $1. Find the expected
value (to you) of the game.
A) $0.39
B) $1.25
C) $0.09
D) $0.00
E) -$0.50

1. Game of rolling dice
a. Roll a fair die once. What is the sample space? What is the
probability to get “six”? What is the probability to get “six” or
“five”?
b. Roll a fair die 10 times. What is the probability to get
“six” twice? What is the probability to get six at
least twice?
c. Roll a fair die 10 times. What is the expected value and
variance of getting “six”?
d. If you roll the die...

. 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.

Roll two dice (one red and one white). Denote their outcomes as
X1 and X2. Let T = X1+X2 denote the total, let X1 W X2 denote the
maximum and let X1 V X2 denote the minimum. Find the following
probabilities: (a) P(X1 ≥ 3|X2 ≤ 4) (b) P(T is prime) (c) P(T ≤
8|X1 W X2 = 5) (d) P(X1 V X2 ≤ 5|T ≥ 8) (e) P(X1 W X2 ≥ 3|X1 W X2 ≤
3)

You roll a pair of fair dice repeatedly. Let X denote the number
of rolls until you get two consecutive sums of 8(roll two 8 in a
row). Find E[X]

Suppose you play a betting game with a friend. You are to roll
two fair 6-sided dice. He says that if you roll a 7 or 11, he will
pay you $100. However, if you roll anything else, you owe him $20.
Let x denote the discrete random variable that represents the
amount you are paid, i.e., x = $100, and the amount you have to
pay, i.e., x = −$20.
Create a table for the probability distribution of x....

Roll a pair of fair dice. Let X be the number of ones in the
outcome and let Y be the number of twos in the outcome. Find
E[XY].

a. Roll a dice, X=the number obtained. Calculate E(X), Var(X).
Use two expressions to calculate variance.
b. Two fair dice are tossed, and the face on each die is
observed. Y=sum of the numbers obtained in 2 rolls of a dice.
Calculate E(Y), Var(Y).
c. Roll the dice 3 times, Z=sum of the numbers obtained in 3
rolls of a dice. Calculate E(Z), Var(Z) from the result of part a
and b.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 17 minutes ago

asked 30 minutes ago

asked 37 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago