Mean of a Discrete Probability Distribution

Introduction to Mean of Discrete Probability Distribution

• Learning Target:
  • To illustrate and calculate the mean of a discrete probability distribution.

Definitions

• Mean (𝜇): The expected value (E(X)) of a discrete random variable.
  • Formula:
    \mu = E(X) = \sum [X \cdot P(X)]
  • Where:
  • \mu = mean
  • X = value of the random variable
  • P(X) = probability of the random variable

Example Calculation

• Given the following probability distribution:
  • | X | P(X) |
    |---|-------|
    | 3 | 1/8 |
    | 2 | 3/8 |
    | 1 | 3/8 |
    | 0 | 1/8 |

Steps to Calculate the Mean

1. Multiply each value of X by its corresponding probability P(X):

   • Create a table:

• Complete the following table to find the mean of the new probability distribution:
  • | X | P(X) | X•P(X) |
    |---|--------|-------|
    | 2 | 0.042 | |
    | 3 | 0.010 | |
    | 4 | 0.021 | |
    | 5 | 0.375 | |
    | 6 | 0.188 | |
    | 7 | 0.344 | |
    | 8 | 0.021 | |

Follow the steps demonstrated in the example to find the expected mean value again.

Conclusion

• The mean of a discrete probability distribution represents the average outcome one can expect from the random variable weighted by their probabilities.