Mean and Variance of Discrete and Continuous Random Variables

A discrete random variable takes on a finite or countable number of possible values.
The mean and variance for discrete random variables are calculated based on the probability of each possible outcome.

1. R19AD251 - Data Science Mean and Variance of Discrete and Continuous Random Variables

2. 1. Discrete Random Variable A discrete random variable takes on a finite or countable number of possible values. The mean and variance for discrete random variables are calculated based on the probability of each possible outcome.

3. Mean (Expected Value) of a Discrete Random Variable The mean or expected value E(X) of a discrete random variable X is the weighted average of all possible values of the variable, where the weights are the probabilities associated with those values.

4. Variance of a Discrete Random Variable

5. Variance of a Discrete Random Variable

6. example

7. 2. Continuous Random Variable A continuous random variable takes on an infinite number of possible values within a given range. The mean and variance for continuous random variables are calculated using integrals since the probability density function (pdf) defines probabilities over intervals.

8. Mean (Expected Value) of a Continuous Random Variable

9. Variance of a Continuous Random Variable

10. Variance of a Continuous Random Variable

11. Example

12. Key Differences