In plain english, summarise the relationship between the exponential, poisson, and gamma distributions
The poisson tells you how many in a certain amount of time. The exponential tells you how long till the first. The gamma tells you how long till the kth.
| Distribution | Can be Special Case Of | Conditions or Parameters |
|---|---|---|
| Exponential | Gamma | Shape parameter of 1 |
| Poisson | Binomial | Number of trials → ∞, probability of success → 0, product remains constant |
| Bernoulli | Binomial | Number of trials is 1 |
| Normal | Binomial | Large number of trials, probability of success not close to 0 or 1 |
| Normal | Poisson | Mean → ∞ |
| Geometric | Negative Binomial | Number of successes is 1 |
| Chi-Square | Gamma | Shape parameter is ( k/2 ), scale parameter is 2 |
| Erlang | Gamma | Shape parameter is an integer |
| Uniform | Beta | Both parameters equal to 1 |
| Standard Normal | Normal | Mean of 0, standard deviation of 1 |
| Rectangular (Uniform) | Triangular | Mode (peak) is anywhere between the minimum and maximum values |
| Log-Normal | - (Related to Normal) | Natural logarithm of the variable is normally distributed |
What is the distribution of the sum of two Uniform(0, 1) random variables?
↳ How could you verify this with a computer?
What is the distribution of a Poisson where you lose _____.
QX) Draw the distribution of the 3rd largest number in a sample of 10 () from a sample of 10 from a distribution with the following pdf
