The geometric random variable
The geometric random variable
The geometric random variable is used when one is modelling a series of experiments that have one of two possible outcomes - sucess or failure. The geometric random variable tells you the number of experiments that were performed before obtaining a sucess. This random variable can thus take values of 1, 2, 3, ... The probability mass function for the geometric random variable is given by: $$ f_X(x) = P(X=x) = (1-p)^{x-1} p $$ The expectation and variance for this random variable are $\mathbb{E}(X) = \frac{1}{p}$ and $\textrm{var}(X) = \frac{1-p}{p^2}$ respectively.
Syllabus Aims
- You should be able to explain what types of phenomena can be modelled using the geometric random variable.
- You should be able to write out the probability mass function for the geometric random variable and explain how this expression is derived by using a tree diagram.
- You should be able to calculate the elements of the probability distribution function for the geometric random variable from the probability mass function.
- You should be able to show that the probability mass function for the geometric random variable is properly normalised.
- You should be able to derive expressions for the mean and the variance of the geometric random variable using the condition expectation theorem.
Description and link | Module | Author | ||
| A video explaining the derivation of the geometric random variable | SOR3012 | G. Tribello |
Description and link | Module | Author | ||
| Problems involving the geometric random variable | SOR3012 | G. Tribello |
Description and link | Module | Author | ||
| Writing a short project on geometric random variables that includes some small programming components. | SOR3012 | G. Tribello |
Contact Details
School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN
Email: g.tribello@qub.ac.uk
Website: mywebsite