[prev] [prev-tail] [tail] [up]

2.5.2 Discrete Probability Distribution

Knowledge Base > Math> Probability Theory

Certain random variables occur very often in probability theory because they well describe many natural or physical processes. A probability distribution gives probability values for all possible values of a random variable. A probability distribution must satisfy

0 ≤ P (x) ≤ 1 ∑ P (x) = 1 x∈Domain(X)
For example, P(Cavity) = <True, False>, or P(Weather = sunny, rain, cloudy, snow) = <0.72, 0.1, 0.1, 0.08>

A joint probability distribution for a set of random variables gives the probability of every atomic event on those random variables, that is, every combination of the values of the st of random variables. A joint probability distribution must satisfy
0 ≤ P (-→x) ≤ 1 ∑ -→ P (x) = 1 -→x∈Domain(-→X)
The joint probability distribution of Weather and Cavity, for example, would produce a 4 times 2 matrix of values.
Note that Every question about a domain can be answered by the joint distribution because every event is a sum of sample points.

[prev] [prev-tail] [front] [up]