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two fair dice are rolled. find the joint probability mass function of x and y when

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Karol A.
Karol A.Lv10
21 Mar 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

When two six-sided dice are rolled there are 36 possible outcomes. Find the probability that

(a) the sum is not 4 and

(b) the sum is greater than 5.

Rules of dice game:

• All players start with 10 points

• A dice is rolled, and if the number on the dice is 1, 2, 3, 4 or 5, this number is added to each player's score. If the number is 6, the score off all players is reduced to zero

• Before the dice is rolled each player is given the choice of continuing or taking their current score as their final score.

• This process is repeated until a 6 is rolled and the game ends. All players still playing at this point receive zero as their final score.

Suppose that you choose to play the first dice roll.

(i) Compute the expected value and standard deviation of your score after the first dice roll.

(ii) On average, do you do worse or better than someone who choose not to play and take 10 as their final score?

Now suppose that a 6 was not rolled and you chooses to continue playing

(iii) On average, what score would you have before the dice is rolled?

(iv) Compute the expected value for your score after the second dice roll.

(v) On average, do you do worse or better than someone who choose to stop playing after 1 dice roll?

(vi) Is there an optimal number of dice rolls you should continue playing for? Explain your reasoning.

(vii) If the rules are changed such that when the number is 2, 3, 4, 5 or 6, this number is added to your score. While if the number is 1, your score is reduced to zero. Discuss how this affects the optimal number of dice rolls you should continue playing for.

Make a probability distribution for the given set of events. The sums that appear when two fair four-sided dice (tetrahedrons) with sides 1, 2, 3, and 4 are tossed. Complete the probability distribution below.

Sum Probability
2  
3  
4  
5  
6  
7  
8  

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