Introduction to probability
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2.1Random variables
A random variable may be discrete orcontinuous.
2.2Joint probability
P(x,y) is the probability ofx and y.Summing over discrete variables and integrating over continuous ones isalways one.
2.3Marginalization
Therecovered distributions are referred to asmarginal distributions, and the process of integrating / summing over the othervariables is called marginalization.
2.4 Conditional probability
tells us the relativepropensity of the random variable x to take different outcomes given that therandom variable y is fixed to value .
2.5Bayes rule
2.6Independence
If knowing the value of variable x tells usnothing about variable y then we say x and y are independent.
2.7Expectation
The expected value of a function of a random variable xis defined as
Thereare four rules for manipulating expectations:
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