This is a draft cheat sheet. It is a work in progress and is not finished yet.
Probability
probability |
a measure of the likelihood of an event |
experiment |
any process resulting an observation or outcome |
sample space |
a set of all possible outcomes of an experiment |
tree diagram vs cross table vs venn diagram |
probability rules |
PA [0,1] |
sum(PA)=1 |
odds in favor of an event: P(A):P(A') |
complement: PA = 1-PA' |
union: P(A)+P(B)+P(AB) |
intersect: P(A)P(B|A)=P(B)P(A|B) |
conditional event: P(A|B)=P(AB)/P(B) |
independent: P(AB)=P(A)*P(B), P(A)=P(A|B), P(B)=P(B|A) |
disjoin/exclusive: interrsect is 0 |
example:shopper items vs gender
autoinsurance: collision protection vs involved in accident
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random variables and their prob distribution
variable |
a quantity whose value varies from subject to subject |
probability experiement |
an experiment with possible outcomes maybe known, but exact outcome is a random event, no certainty could be predict in advance |
random variable |
outcome of a probability experiment is numeric |
discrete random variable |
quantitative variable that takes a countable number of values |
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could you have half unit of your variable? No |
continuous random variable |
quantitative variable that can take all the possible values in a given range |
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could you have half unit of your variable? Yes |
discrete random variable distribution
Probability distribution of discrete random variables |
table{ X,p(xi) } |
P(xi) [0,1] sum(P(xi)=1 |
Mean/expected value |
E(X)=sum(xi*P(xi)) |
variance |
sum((xi-mean)2*P(xi) ) |
standard deviation |
expected values for how much any given data point will vary from the mean |
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