The poisson random variable
The poisson random variable
The probability mass function for a Poisson random variable is: $$ f_X(x) = P(X=x) = \frac{\lambda^x}{x!} e^{-\lambda} $$ where $\lambda$ is a parameter. The expectation and variance of this random variable are $\mathbb{E}(X) = \lambda$ and $\textrm{var}(X) = \lambda$.
Syllabus Aims
- You should be able to explain how the Poisson distribution can be derived from the binomial distribution in the limit as $n \rightarrow \infty$
- You should be able to write out the probability mass function for the Poisson random variable.
- You should be able to show that the Poisson random variable is properly normalised.
- You should be able to derive the moment generating functions for the poisson random variable and hence obtain the expectation and variance for this random variable
Description and link | Module | Author | ||
| Problems involving the Poisson Random variable. | SOR3012 | G. Tribello |
Description and link | Module | Author | ||
| Writing a short project on poisson 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