Bob plays a game in which he rolls a pair of fair 6-sided dice once. He...

Question

Question

Bob plays a game in which he rolls a pair of fair 6-sided dice once. He adds the number of dots on both dice to create a sum. He

loses $1 if he rolls a sum less than 5
doesn’t win or lose anything if he rolls a sum that is higher than 4, but less than 8
wins $1 if he rolls a sum that’s higher than 7 but less than 12
wins $2 if he rolls a sum of 12

a. If X is a random variable indicating Bob’s earning, write the PMF of X in a table.

b. If Y = X2 + 1, write a table for the PMF of Y.

Answer 1

Answer #1

let A is outcome on dice ,

a)

below is pmf of X:

P(X=-1)=P(getting a sum less then 5)=P(A=2)+P(A=3)+P(A=4)=(1/36)+(2/36)+(3/36)=1/6

P(X=0)=P(5<=A<=7)=P(A=5)+P(A=6)+P(A=7)=(4/36)+(5/36)+(6/36)=15/36=5/12

P(X=1)=P(A=8)+P(A=9)+P(A=10)+P(A=11)=(5/36)+(4/36)+(3/36)+(2/36)=14/36=7/18

P(X=2)=P(A=12)=1/36

b)

Y = X^2 +1

P(Y=1)=P(X=0)=5/12

P(Y=2)=P(X=-1)+P(X=1)=1/6+7/18=20/36=5/9

P(Y=5)=P(X=2)=1/36

Answer 2

Similar Homework Help Questions

Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if...

Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if the sum of his dice is six, then he wins the game. If not, then Doug rolls the dice, and if the sum of his rolls is seven, then he wins the game. If neither player wins the game during the first round, then they repeat the process (with Bob going first) until someone wins a round. What is the probability that Bob wins...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is all...

Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
1 point) Three brothers play a game with a pair of fair (six-sided) dice. Scott will...

1 point) Three brothers play a game with a pair of fair (six-sided) dice. Scott will win if the sum of the dice is 3, Dave will win if 9, and Jim if 11 They will roll the die until a winner is declared Part (c) Realizing this, theoretically, is a game that could go on forever..the three brothers decide that if no winner has been decided in three rolls or "turns" Scott will be deemed the winner. Let Y...

. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the...

. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet...
Conditional Expectation A player plays a game. A pair of fair dice is rolled, the outcome...

Conditional Expectation A player plays a game. A pair of fair dice is rolled, the outcome of the Red die is denoted by R and the outcome of the Yellow die is deonted by Y. The player does not get to see the outcome of each die but is told the total sum of the two dice, denoted S. She wins W = $10 if the two dice have the same value (like Y = 4, R = 4 or...
Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly...

Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly rolled. If a ’ 7 ’ comes up before an ’ 11 ’ , then the player wins, otherwise the player loses. Let W be the event that the player wins. Find P(W). To say the dice are fair is equivalent to assuming that Laplace’s rule holds and the 36 possible outcomes for a throw of the dice are equally likely. For convenience, an...

the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum...

the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet $1 that...
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than...

Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than or equal to 4 is rolled once again. Let X be the number of dice that show a number less than or equal to 4 on the first roll, and let Y be the total number of dice that show a number greater than 4 at the end. (a) Find the joint PMF of X and Y . (Show your final answer in a...
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting...

In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, using method one, the player can bet $2.00 that the sum will be under 7, that is, 2, 3, 4, 5, or 6. For this bet, the player wins $2.00 if the result is under 7 and loses $2.00 if the outcome equals or is greater than 7. Similarly, using...

The game of Pig is a simple two-player dice game in which the first player to...

The game of Pig is a simple two-player dice game in which the first player to reach 100 or more points wins. Players take turns. On each turn, a player rolls a six-sided die: If the player rolls a 1, then the player gets no new points and it becomes the other player’s turn. If the player rolls 2 through 6, then he or she can either ROLL AGAIN or HOLD: At this point, the sum of all rolls...