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Roll a die twice and let Y be the sum of the two rolls. Find the...

Roll a die twice and let Y be the sum of the two rolls. Find the joint pmf of (X, Y ) if X is

(a) the number on the first roll

(b) the smallest number

Math   Statistics-And-Probability   
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Answer #1

if we carefully observe the outcomes you can understand the probability values obtained in both the pmfs.

probability is the number of outcomes that satisfy the condition given you the number of outcomes (36).

for example the sum should be 6 and first number x= 2 we have (2,4) combination which yields a sum of 6 with 2 as the number in the first roll. therefore p= 1/36.

the sum y=8 and smallest number of two rolls x= 3 we have (3,5) and (5,3) which yields sum as 8 therefore p=2/36 or 1/18

hope you understand any query please comment below thank you:)

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