qt1 - 06 - normal distribution
Post on 16-Apr-2017
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Probability Distributions
Normal Distributions
QUANTTECHINTEUQIASEVIT10S
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
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