MS&E 4040 – Fall 2011 - HW #11. Rolling ofNdice and summing the pips generates a probability distribution for values bewteenNand 6N.Obviously forN= 1 the distribution is a constant with 1/6 for each value.Consider thecase ofN= 5. Calculate exactly the probability distribution for each value, plot as a histogram andcompare to a Gaussian probability. The average is easy to determine, but the standard deviation forthe 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 thatthe total payoff is equal to the total amount paid. Basically the customer rolls a set of five Yahtzeedice 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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