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# hw#1a - MS&E 4040 Fall 2011 HW#1 1 Rolling of N dice and...

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MS&E 4040 – Fall 2011 - HW #1 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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