Probabilities

probability rules, distribution (discrete vs continuous), random processes,

probability

quantify uncertainty in regression analysis

probability distribution

assigns probability to outcomes of a random variable

As n → ∞

empirical distribution → theoretical distribution

discrete distribution

outcomes countable

continuous distribution

outcome can take any value in a range

normal distribution

X ~ N(µ,∂²), spread controlled by sd (∂), symmetric about mean

random process

unpredictable outcome

outcome

single specific result

sample space

complete set of all possible outcomes

random event

subset of sample space

Union (or)

A U B

Intersection (and)

A n B

complement (not)

A^c

disjoint

A n D = ø

if A n B = ø

P(A U B) = P(A) + P(B)

P(A U B) (non-disjoint)

P(A) + P(B) - P(A n B)

conditional probability P(B|A)

P(A n B)/P(A)

P(A n B) (conditional probability)

P(B|A) * P(A)

P(B|A) (independence of variables)

P(B) → P(A n B) = P(A) * P(B)