MATH 1040 - Introduction to Statistics

12.1 Probability Distributions

Reading

Reading sections are from the Introductory Statistics Textbook

Probability Distribution

The core of all distributions is the probability distribution. A probability distribution simply describes the frequency of times each possible outcome of a given event occurs. For example, here is a distribution showing how many people in each age group attended an event:

Age	0-4	5-9	10-14	15-19	20-24	25-29	30-34
Count	10	15	12	25	29	32	23
Frequency	0.068	0.103	0.082	0.171	0.199	0.219	0.158

This shows how all subjects in our sample are distributed through all categories.

There are two very important rules for probability distributions:

Each probability has to be between 0 and 1
All probabilities have to add up to 1

If one of these rules is broken, then we have an invalid probability distribution.

Practice

Here is a probability distribution with one missing value. Determine what that value should be.

Category	A	B	C	D	E	F
Probability	0.08	0.16	0.22	0.34	0.18	x

After solving on your own, check the solution.

Here are three distributions. One of them is invalid. Determine which is the invalid distribution and what can be done to fix it.

Distribution 1	A	B	C	D	E	F
Probability	0.05	0.12	0.15	0.18	0.23	0.27

Distribution 2	A	B	C	D	E	F
Probability	0.14	0.20	0.24	0.22	0.14	0.09

Distribution 3	A	B	C	D	E	F
Probability	0.17	0.17	0.16	0.16	0.17	0.17

After solving on your own, check the solution.

Here are three distributions. One of them is invalid. Determine which is the invalid distribution and what can be done to fix it.

Distribution 1	A	B	C	D	E	F
Probability	0.24	0.28	0.24	0.19	-0.11	0.16

Distribution 2	A	B	C	D	E	F
Probability	0.04	0.09	0.13	0.16	0.26	0.32

Distribution 3	A	B	C	D	E	F
Probability	0.13	0.17	0.24	0.21	0.16	0.09

After solving on your own, check the solution.