Discrete and Continuous Random Variables (AQA A-Level Further Maths): Flashcards

Poisson distribution

$P(X = x) = \frac{e^{-\lambda}\lambda^x}{x!}$

$X \sim \text{Po}(\lambda)$

Mean = variance = $\lambda$

RICE: Random, Independent, Constant rate, Events don't overlap

Check if mean ≈ variance

$X + Y \sim \text{Po}(\lambda_x + \lambda_y)$

$n\lambda$

Mean number of occurrences in the given interval

$\sqrt{\lambda}$