"Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs is pencil and paper." -- (D. J. Albers and G. L. Alexanderson, Mathematical People ) Triskaidekaphobia: This is fear of the number 13. Interestingly, no one really knows how this developed. It has been suggested that it might be related to the Biblical Last Supper, but there is no real evidence that this is the source. Mark 14: 17-21 And it was in the evening he came with the twelve. And as they were at the table eating, Jesus said "Truly, I say to you, one of you will betray me, one who is eating with me." They began to be sorrowful, and to say to him one after another, "Is it I?" He said to them, "It is one of the twelve, one who is dipping in the same dish with me. For the Son of man goes as it is written of him, but woe to that man by whom the Son of man is betrayed! It would have been better for that man if he had not been born." The inference is that one in the group of 13 is doomed. Famous people who would not dine in a group of 13 include Napoleon, Paul Getty, and Franklin Delano Roosevelt. It is easy to prove that every year must have at least one Friday the 13th. What does Herkimer call a window that has been installed in a glass building? Answer: A pane in the glass. Herky's friends: WILLIE MAKEIT... everybody wonders if the guy can be successful. MILLIE METER... she believes the U.S. should convert to the metric system. ASSIGNMENT #43 Reading: Review Chapter 7 material, as necessary Exercises: The ones previously assigned, plus a good description of your game.

You are working with ideas from Chapter7.

The game of KENO (a summary of 3-SPOT KENO asplayed at John Ascuaga's Nugget, Reno.

• You pay \$1 to play. You then pick three numbers from the set S ={1,2,3,...,78,79,80}.
• House then randomly picks twenty numbers from this set.
• If two of your numbers are among the twenty, you win \$1.
• If three of your numbers are among the twenty, you win \$42.
• Note: You don't get your "invested" dollar back (as you do in roulette), when you win.

Here are probabilities associated with 3-SPOTKENO

 Match Probability Player Expectation (dollars) 0 (3C0)(77C20)/(80C20) = 0.4165 -1 1 (3C1)(77C19)/(80C20) = 0.4309 -1 2 (3C2)(77C18)/(80C20) = 0.1388 0 3 (3C3)(77C17)/(80C20) = 0.0139 41

We can define two different random variables here. One is X, which will be defined as player's gain in terms of dollars. The set containing all possible values of X is {-1,0,41}. The mean of the X values is

E(X) = (-1)(.8474) + (0)(.1338) + (41)(.0139) = -0.2365.

In other words, a player who "invests" \$1 can expect a return of about \$0.76.

Another random variable is M, the number of matches. The set containing all values of M is {0,1,2,3}. The mean of the M values is

E(M) = (0)(.4165) + (1)(.4309) + (2)(.1388) + (3)(.0139) = 0.7502.

To my knowledge, E(M) is not particularly meaningful, but E(X) certainly is!!!

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Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)