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In Example 2.2-1 let Z = u(X) = X3. (a) Find the pmf of Z, say h(z). (b) Find E(Z). (c)
Chapter 2, Problem 2.2-5(choose chapter or problem)
In Example 2.2-1 let Z = u(X) = X3. (a) Find the pmf of Z, say h(z). (b) Find E(Z). (c) How much, on average, can the young man expect to win on each play if he charges $10 per play?
Questions & Answers
QUESTION:
In Example 2.2-1 let Z = u(X) = X3. (a) Find the pmf of Z, say h(z). (b) Find E(Z). (c) How much, on average, can the young man expect to win on each play if he charges $10 per play?
ANSWER:Step 1 of 4
Given that,
From the given example 2.2-1, we know that
An enterprising young man who needs a little extra money devises a game of chance in which some of his friends might wish to participate. The game that he proposes is to let the participant cast a fair die and then receive a payment according to the following schedule:
If the event A = {1, 2, 3} occurs, he receives one dollar.
If B = {4, 5} occurs, he receives two dollars.
If C = {6} occurs, he receives three dollars.
If X is a random variable that represents the payoff, then the pmf of X is given by
