Marginal Density Function
For joint probability density function for two random variables X and Y, an individual probability density function may be extracted if we are not concerned with the remaining variable. In other words, the marginal density function of x from f (x, y) may be attained via:
Example:
Based upon the joint probability density function for two discrete random variables X and Y, determine the marginal density functions for x and y.
| Y = 1 | Y = 2 | Y = 3 | Y = 4 | Y = 5 | |
| X = 1 | 0 | 0 | 0.2 | 0 | 0 |
| X = 2 | 0.1 | 0 | 0 | 0.05 | 0.15 |
| X = 3 | 0 | 0.05 | 0.1 | 0 | 0 |
| X = 4 | 0 | 0 | 0 |
0 | 0 |
| X = 5 | 0.1 | 0 | 0.05 | 0.1 | 0.1 |
Solution:
