You roll a fair, six-sided die as part of a game. If you roll a 5, you will win the game.
a. What do you consider a "success" in this story? What is its probability?
b. What do you consider a "failure" in this story? What is its probability?
c. Why is this a Bernoulli situation? What is the parameter?
d. Define in words what X is in terms of this story. What values can X take?
e. Your friend will pay you $4 if you win the game. You owe your friend $1 if you lose the game. What are your expected winnings?
f. What is the variance of your expected winnings?