A game called Wordle, an online game where you must correctly guess a five-letter word within six attempts. Let Y represent the number of attempts it takes to get the right guess

y	2	3	4	5	6
p(y)	0.03	0.1	0.47	0.74	?

(a) Assume the first attempt is always wrong, but able to always get the right guess it by the sixth attempt. What is p(6)? (b) Find the expected value of Y and interpret it. (c) Find the variance of Y. (d) Scott has an ongoing bet with Tom.

Tom will give Scott $50 if he correctly guesses the word on the first attempt, but Tom will remove $15 from the prize pool for each failed attempt. If this amount becomes negative, then Scott will need to pay Tom money.

For example, if it takes Scott six attempts to guess the word, then he will owe Tom $25. Let X represent Scott's winnings in this game. Write X as a function of Y and use the properties of expected values to determine Scott's long-run average winnings per game. Do not use a computation like what you did in part (b)

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