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Chapter 7

SPAN 101 Chapter Notes - Chapter 7: Bernoulli Trial, Simple Random Sample, Unimodality

Course Code
SPAN 101
Enrique Manchon

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Law of large numbers: relative frequency of a random event settles down to a single
number in the long run
Different Types of probability
Model based (theoretical) probability:
o Empirical probability the relative frequency of an event’s occurrence as the
probability of an event
o P(A) = # of outcomes in A / total # of outcomes
Personal Probability:
o Personal assessment of an event expresses your uncertainty about the
o Not based either on long run relative frequencies or equally likely events
o Satisfy the same rules as both empirical and theoretical probabilities
Probability Rules:
Rule 1: a probability is a number between 0 & 1.
0<= P(A) <=1
Rule 2: probability assignment rule: the probability of the set of all possible
outcomes must be 1
P(S) = 1 ; where s represents the set of all possible outcomes
Rule 3:the set of outcomes that are not in the event A is called complement of A, Ac
Complement Rule: the probability of an event occurring is 1 minus the probailtiy
that it doesn’t occur
P(A) = 1 P(AC)
Rule 4: multiplication rule: for 2 independent events A and B, the probability that
both A and B occur is the product of the probabilities of the 2 events
P(A and B) = P(A) x P(B), A and B are independent
Rule 5: addition Rule: add the probabilities of disjoint events to get the probability
that either event occurs:
P(A or B) = P(A) + P(B)
Rule 6: General Addition Rule: add the probabilities of two events and then subtract
the probability of their intersection
P(A or B) = P(A) + P(B) P (A and B)
Marginal probability: only totals found in the margins of the table
Joint probability: probability of two events occurring together
Conditional probability: takes into account a given condition
P(B|A) = P(A and B) / P(A)
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