Risk analysis and Standard Deviation. Consider the following two games: Game 1: Toss a fair coin once. If it comes up Heads, you win $100. If it comes up tails, you lose nothing--zero dollars. Expected Value or ? = Standard Deviation or ? = There are only two two possible values--$0 or $100 (each with probability 0.5). Game 2: Toss a fair coin a hundred times. For each Heads that comes up, you win $1 and for tails you lose nothing. The amount of dollars is equivalent to the number of Heads that turn up. This can be viewed in terms of Binomial Probabilities, with p = q = 0.5 and n = 100 (See Section 5.3, page 232 of the textbook). Expected Value or ? = Standard Deviation or ? = Standard Deviation measures the "risk" of the two games. Since the Standard Deviation of Game 2 is lower than that of Game 1, Game 2 is "less risky". This can be further analyzed by calculating the usual values in Game 2 (See Section 5.3, page 233 of the textbook. Also Problem 5 on page 237 is relevant.). Here "usual" means "happens at least 95% of the time". Usual values of dollars earned are in between (lower end) = $ and (upper end)
Risk analysis and Standard Deviation.
Consider the following two games:
Game 1: Toss a fair coin once. If it comes up Heads, you win $100. If it comes up tails, you lose nothing--zero dollars.
Expected Value or ? =
Standard Deviation or ? =
There are only two two possible values--$0 or $100 (each with probability 0.5).
Game 2: Toss a fair coin a hundred times. For each Heads that comes up, you win $1 and for tails you lose nothing.
The amount of dollars is equivalent to the number of Heads that turn up. This can be viewed in terms of Binomial Probabilities, with p = q = 0.5 and n = 100 (See Section 5.3, page 232 of the textbook).
Expected Value or ? =
Standard Deviation or ? =
Standard Deviation measures the "risk" of the two games. Since the Standard Deviation of Game 2 is lower than that of Game 1, Game 2 is "less risky". This can be further analyzed by calculating the usual values in Game 2 (See Section 5.3, page 233 of the textbook. Also Problem 5 on page 237 is relevant.). Here "usual" means "happens at least 95% of the time".
Usual values of dollars earned are in between (lower end) = $ and (upper end) = $
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