A spinner from a board game randomly indicates a real number between 0 and 20. The...
A spinner from a board game randomly indicates a real number between 0 and 20. The spinner is fair in the sense that it indicates a number in a given interval with the same probability as it indicates a number in any other interval of the same length.
(a) Explain why the functionf(x) =
f(x)= |
| 0.05 | if | 0 ≤ x ≤ 20 |
| 0 | if | x < 0 or x > 20 |
is a probability density function for the spinner's values? ______________________________
(b) What does your intuition tell you about the value of the mean,
μ? Check your guess by evaluating an integral.
μ = ________
Homework Answers
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A spinner from a board game randomly indicates a real number
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Problem 3.4 (10 points) Consider this game of chance with a monetary payoff. First, a real number is chosen uniformly at random from the interval [0,10]. Next, an integer X is chosen according to the Poisson distribution with parameter U. The player receives a reward of SX What would be the fair price charged for playing this game? That is, how much should it cost to play so that expected net gain is zero?
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2. One the last exam, you analyzed a mini-version of the board game Chutes and Ladders. For your reference, this information is repeated on the next page. (a) Give the one-step transition matrix P for the Markov chain {Xn,n 2 0]. (This is the same question that was on the exam) (b) What is the expected length (number of spins) of a game? (c) In which square should the player expect to spend the most time? (d) In which square...
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