1. Rolling of N dice and summing the pips generates a probability distribution for values bewteen N and 6 N . Obviously for N = 1 the distribution is a constant with 1 / 6 for each value. Consider the case of N = 5. Calculate exactly the probability distribution for each value, plot as a histogram and compare to a Gaussian probability. The average is easy to determine, but the standard deviation for the distribution will require calculation or ﬁtting. 2. In Wisconsin, almost all of the locals play a game with the bartender. This is a “fair” game in that the total payoﬀ is equal to the total amount paid. Basically the customer rolls a set of ﬁve Yahtzee dice trying to get speciﬁc patterns (no multiple rolls - must be “neat”). The speciﬁc rules are: • It costs $1.00 to play, with the money going into a pool • The winnings are paid from the pool • The customer gets to roll the dice three times trying to win • The winning events are: – Full House - free drink (a $3 value)
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This note was uploaded on 09/29/2011 for the course MSE 4040 at Cornell University (Engineering School).