random process: we know what outcomes could happen, but we don’t know which particular outcome will happen
two ways to interpret probability
law of large numbers
disjoint events(mutually exclusive) cannot happen at the same time. p non-disjoint events
for disjoint events A and B, union of disjoint events P(A or B)=P(A)+P(B)
union of non-disjoint events P(J or red) = P(J)+P(red)-P(J and red)
general addition rule: P(A or B) = P(A) +P(B)-P(A and B)
sample space a collection of all possible outcomes of a trial
a probability distribution lists all possible outcomes in the sample space and the probabilities with which they occur
rules of probabilities distribution
complementary events: two disjoint event which sum up to 1.
disjoint -> complementary
two precesses are independent if knowing the outcome of one provides no useful information about the outcome of the other.
knowing B tells nothings about A P(A|B) = P(A) where A and B are independent.
product rule for independent events: P(A and B) = P(A)*P(B)
when choose sample, random select means the samples are independent
marginal probability joint probability conditional p
calculate condition p based on the bayed’s theorem:
bayes inference
bayes inference
二项分布的标准差
σ=np(1−p)‾‾‾‾‾‾‾‾‾√
\sigma = \sqrt{np(1-p)}
二项分布与正泰分布的转换