Course Content
Probability Theory Mastering
1. Additional Statements From The Probability Theory
3. Estimation of Population Parameters
4. Testing of Statistical Hypotheses
Probability Theory Mastering
Absolutely Continuous and Discrete Random Variables
Understanding Random Variables
A random variable is a value that changes based on the outcome of a random event or experiment. For example, it could be the number of heads in coin tosses, accidents on a road segment, weight on a scale, or bus wait time.
Random variables can be categorized into two types:
- Discrete Variables: Take specific, countable values like natural numbers (e.g., the number of road incidents);
- Continuous Variables: Can take any value within a certain range (e.g., a person's weight).
| Discrete random variables | Continuous random variables |
|---|---|
| Number of tails that fell out | The result of weighing on the scales |
| Number of accidents on the road | Bus waiting time |
| Number of hits on the target during shots | The height of a person |
Probability Mass Function (PMF)
Probability Mass Function (PMF) is used to describe discrete random variables. It's like a table containing all possible values of the random variable and their corresponding probabilities.
For example, consider a simple PMF describing the outcome of a single coin toss.
| Experiment result | Head | Tail |
|---|---|---|
| Probability | 0.5 | 0.5 |
Let's look at the example of using PMF in Python: we will use the Binomial distribution described in the Probability Theory Basics course.
The result of the code above can be represented as follows:
| Number of heads | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Probability | 0.0312 | 0.1562 | 0.3125 | 0.3125 | 0.1562 | 0.0312 |
Note
The sum of all probabilities in the PMF table always equals 1.
On the other hand, how can we represent continuous random variables if we cannot simply list all possible values of these variables and write down the distribution series? We will address this question in the next chapter.
Choose discrete random variables from the list:
Select a few correct answers
Everything was clear?
Course Content
Probability Theory Mastering
1. Additional Statements From The Probability Theory
3. Estimation of Population Parameters
4. Testing of Statistical Hypotheses
Probability Theory Mastering
Absolutely Continuous and Discrete Random Variables
Understanding Random Variables
A random variable is a value that changes based on the outcome of a random event or experiment. For example, it could be the number of heads in coin tosses, accidents on a road segment, weight on a scale, or bus wait time.
Random variables can be categorized into two types:
- Discrete Variables: Take specific, countable values like natural numbers (e.g., the number of road incidents);
- Continuous Variables: Can take any value within a certain range (e.g., a person's weight).
| Discrete random variables | Continuous random variables |
|---|---|
| Number of tails that fell out | The result of weighing on the scales |
| Number of accidents on the road | Bus waiting time |
| Number of hits on the target during shots | The height of a person |
Probability Mass Function (PMF)
Probability Mass Function (PMF) is used to describe discrete random variables. It's like a table containing all possible values of the random variable and their corresponding probabilities.
For example, consider a simple PMF describing the outcome of a single coin toss.
| Experiment result | Head | Tail |
|---|---|---|
| Probability | 0.5 | 0.5 |
Let's look at the example of using PMF in Python: we will use the Binomial distribution described in the Probability Theory Basics course.
The result of the code above can be represented as follows:
| Number of heads | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Probability | 0.0312 | 0.1562 | 0.3125 | 0.3125 | 0.1562 | 0.0312 |
Note
The sum of all probabilities in the PMF table always equals 1.
On the other hand, how can we represent continuous random variables if we cannot simply list all possible values of these variables and write down the distribution series? We will address this question in the next chapter.
Choose discrete random variables from the list:
Select a few correct answers
Everything was clear?
