Let´s suppose that we know all the possible causes for an outcome, for example:
**
Bayes theorem
Posterior = ( Likelihood * Prior ) / Evidence
Here, P(movie|Sci-fi) is called Posterior, P(Sci-fi|Movie) is Likelihood, P(movie) is Prior, P(Sci-fi) is Evidence.
Prior: How probable was our hypothesis before observing the evidence? Posterior: How probable is our hypothesis given the observed evidence? Evidence: How probable is the new evidence under all possible hypotheses? Likelihood: How probable is the evidence give that our hypotheses is true?
The expected value is the mean of the posterior distribution.
$$ P ( A | B ) = \frac { P ( B | A ) P ( A ) } { P ( B ) } $$
We know that in pur favourite TV channel they show 40% of the times drama movies, 50% action and 10% horror movies, we´d like to know the probability that tonight there will be an horror movie P(A = Horror) = 0.1, this is our prior probability.
We check the Calendar and today is Hallowing´s night, in Hallowing the channels in general they show horror movies at least 75% of them P()
Distributions
Discrete: They have only values based on a list of possible values, like the day of the month, number of persons… Continuous: They take arbitrarily exact values, for example prices, weights, distances… Mixed: A Combination of both categories.
Mass and Density Functions
Discrete distributions have probability mass functions while continuous distributions have probability density functions.
Probability Mass Function
The mass function for the Poisson distribution is:
$$ P ( Z = k ) = \frac { \lambda ^ { k } e ^ { - \lambda } } { k ! } , k = 0,1,2 , \ldots $$
Probability Density Function
The density function for an exponential random variable:
$$ f _ { Z } ( z | \lambda ) = \lambda e ^ { - \lambda z } , \quad z \geq 0 $$
Th exponential variable can be continuous not only integers, still only positive numbers.
Next
We’ll be using the following python packages:
