Consider a board game where you move your piece the number of spaces shown on the die.
Let $X$ be the number that is rolled. Complete the probability distribution table.
$x$
$1$
$2$
$3$
$4$
$5$
$6$
$P\left(X=x\right)$
If you roll the die six times, how many times would you expect to roll a 1?
If you roll the die six times, how many times would you expect to roll a 2?
If you roll the die six times, how many times would you expect to roll a 3?
If you roll the die six times, how many times would you expect to roll a 4?
If you roll the die six times, how many times would you expect to roll a 5?
If you roll the die six times, how many times would you expect to roll a 6?
After you roll the die six times, how many spaces would you expect your piece to move in total?
Find the mean number of spaces you would expect your piece to move per roll.
Consider the same board game.
If you roll the die twelve times, how many times would you expect to roll a 1?
If you roll the die twelve times, how many times would you expect to roll a 2?
If you roll the die twelve times, how many times would you expect to roll a 3?
If you roll the die twelve times, how many times would you expect to roll a 4?
If you roll the die twelve times, how many times would you expect to roll a 5?
If you roll the die twelve times, how many times would you expect to roll a 6?
After you roll the die twelve times, how many spaces would you expect your piece to move in total?
Find the mean number of spaces you would expect your piece to move per roll.
Consider the same board game.
If you roll the die eighteen times, how many times would you expect to roll a 1?
After you roll the die eighteen times, how many spaces would you expect your piece to move in total?
Find the mean number of spaces you would expect your piece to move per roll.
Notice how the mean number of spaces was the same regardless of how many times you rolled the die.
This mean value or expected value of a random variable is the average value you would expect after performing the experiment many times.
If you roll the die $n$ times, how many times would you expect to roll a 1?
After you roll the die $n$ times, the number of spaces would you expect your piece to move in total would be:
