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my-statistics-notes.MD

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probability (P)  - numerical value
sample space (S) - well defined SET of possible outcomes (of an experiment)
event (A,B, etc) - well defined SET of          outcomes (of an experiment) with a probability
                   is subset of sample space (S)
experiment       - any procedure that can be infinitely repeated, has a sample space

#1
probability of sample space (S) = P(S) = 1

#2
probability of     occurence of event (A) = P(A)  is beteen 0 and 1, both inclusive, 0<=P(A)<=1
probability of non-occurence of event (A) = P(A') is beteen 0 and 1, both inclusive, 0<=P(A)<=1

P(A) = number of favourable outcomes / total number of outcomes
P(A) = |A| / |S|

if A and A' is S
then P(A) + P(A') = P(S)
  => P(A) + P(A') = 1
  => P(A') = 1 - P(A)


Simple event
Compound event  = combination of simple events

A U B = occurence of A or  B
A n B = occurence of A and B

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

Mutually exclusive (disjoint) events
 = No common outcomes of between A and B
  A n B  = Pi (empty set)
P(A n B) = 0

   P(A U B) = P(A) + P(B) - P(A n B)
=> P(A U B) = P(A) + P(B) - 0
=> P(A U B) = P(A) + P(B)