A fair die is rolled. If the top face is a 5 or 6, you win $1; otherwise you win nothing. Let 
be the amount you win in one play of the game and let 
be the average amount you win in two plays of the game. Find the sampling distribution of 
.
Definitions:
Sample Mean
The average value calculated from a sample of a population.
Sampling Distribution
The probability distribution of a statistic obtained through a large number of samples drawn from a specific population.
Simple Random Samples
A subset of a population where every member has an equal chance of being selected, ensuring unbiased representation.
Standard Error
A measure of the sampling variability of an estimator, indicating the uncertainty around the estimate of a population parameter.
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