Download Probability Distributions Math 121 - Workshop 1. Make a list of all

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