Probability Distributions

Normal Distributions

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Continuous Random Variable

Discrete Variables

Bernoulli

Binomial

Poisson

Random variables can take a fixed number of values, like ...

Integers

Range of integers

Any arbitrary FINITE set

For each value there is a probability of occurrence

Continuous

Exponential

Normal

Random value can take any value, including fractional values, in a range.

This is potentially INFINITE

Between 1 and 2

1.1, 1.2, 1.3 .... 1.9, 2.0

1.1, 1.11, 1.12, 1.13 ..

1.111, 1.112, 1.113 ...

1.1111, 1.1112, 1.1113 ..

Probability of a Continuous Variable

Since an infinite number of random variables are possible, in ANY given range, the probability of any single variable is ZERO!

P(X = x) = 0 !!

However the probability of the variable lying in a range is not zero

P(x < X