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Two fair dice are rolled. Let X represent the number on
Chapter 2, Problem 30SE(choose chapter or problem)
Two fair dice are rolled. Let X represent the number on the first die, and let Y represent the number on the second die. Find \(\mu_{X Y}\).
Questions & Answers
QUESTION:
Two fair dice are rolled. Let X represent the number on the first die, and let Y represent the number on the second die. Find \(\mu_{X Y}\).
ANSWER:Step 1 of 2
It is given that two fair dice are rolled. X denotes the number on the first die and Y denotes the number on the second die.
Then X and Y can take values 1,2,3,4,5,6.
Since the dice are fair, \(\mathrm{P}(\mathrm{X}=\mathrm{x})=\frac{1}{6}\) and \(\mathrm{P}(\mathrm{Y}=\mathrm{y})=\frac{1}{6}\).
We have to find the expected value of the joint probability mass function. That is we have to find \(\mu(X Y)\).