Two fair six-sided dice are rolled. Let X = the largest number that landed facin

Question

Two fair six-sided dice are rolled. Let X = the largest number that landed facing up and Y = the absolute difference between the two numbers that landed facing up.

1) Make a table that gives the joint probability mass function for X and Y.

2) Give the marginal probability mass function for X.

3) Give the marginal probability mass function for Y.

4) What is the probability that the absolute difference between the two numbers rolled is at least two and the largest number rolled was greater than four?

Explanation / Answer

from above

probabilty of a pair =1/36

hence

as each combination have probabilty 1/36 after adding duplicate values below is the joint probability mass function

2) marginal probability mass function for X.

c)  marginal probability mass function for Y.

4) from above table P(X>=4, Y>=2) =9/18=1/2

1st die 2nd die x=max(1,2) y=|1-2| 1 1 1 0 2 1 2 1 3 1 3 2 4 1 4 3 5 1 5 4 6 1 6 5 1 2 2 1 2 2 2 0 3 2 3 1 4 2 4 2 5 2 5 3 6 2 6 4 1 3 3 2 2 3 3 1 3 3 3 0 4 3 4 1 5 3 5 2 6 3 6 3 1 4 4 3 2 4 4 2 3 4 4 1 4 4 4 0 5 4 5 1 6 4 6 2 1 5 5 4 2 5 5 3 3 5 5 2 4 5 5 1 5 5 5 0 6 5 6 1 1 6 6 5 2 6 6 4 3 6 6 3 4 6 6 2 5 6 6 1 6 6 6 0

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