Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Probability Distributions Math 121 - Workshop 1. Make a list of all elements in the sample spaces described below. Then decide if the sample space is equiprobable. (a) The possible outcomes when you flip a fair coin three times in a row. (b) The possible outcomes when you count the total number of heads after flipping a fair coin three times. (c) The result if you roll a six-sided die and flip a fair coin. 2. The table on the left shows the possible outcomes from rolling two six-sided dice and adding the results. Then use the space to the right to make a probability histogram for this random variable. 6 36 + 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 5 6 7 6 7 8 7 8 9 8 9 10 9 10 11 10 11 12 Probability Second Die Result First Die Result 5 36 4 36 3 36 2 36 1 36 2 3 4 5 6 7 8 Outcome 9 10 11 12 3. In the gambling game craps, you roll two six-sided dice and you win if the total is 7 or 11. What is the probability that you win? 4. Below is the probability histogram for rolling three six-sided dice and adding the results. What do you notice about the shape of this probability distribution? 5. The cumulative distribution function (CDF) of a random variable tells you the probability the random variable will have a value less than or equal to a given outcome. For example if you roll three six-sided dice, here is the CDF: Outcome CDF 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.005 0.019 0.046 0.093 0.162 0.259 0.375 0.500 0.625 0.741 0.838 0.907 0.954 0.981 0.995 1.000 (a) Using the CDF above, what is the probability of rolling a 14 or lower? (b) What is the probability of rolling a 15 or higher? 6. Complete the CDF below for rolling two six-sided dice and adding the results. Outcome CDF 2 1 36 3 4 5 6 36 10 36 6 7 8 9 10 11 26 36 30 36 33 36 12