COMMERCE 2QA3 Study Guide - Final Guide: Discrete Uniform Distribution, Probability Mass Function, Unimodality
28 Jun 2018
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Probability
The theoretical probability of event A can be computed by
whenever the outcomes ae
equally likely.
Rule 1:
If the probability of an event occurring is
The event
0
Can't occur
1
Always occur
Between 0 and 1
Rule 2: The Probability Assignment Rule
The probability of a set must be 1, as in
, where represents the set of all possible outcomes and is the
sample space.
Rule 3: Complement Rule
where is the complement of .
Rule 4: Multiplication Rule
For two independent events A and B, the probability that both occur is
Rule 5: Addition Rule
Disjoint or mutually exclusive events have no common outcomes. Adding probabilities of disjoint events gets the
probability that either occur.
Rule 6: General Addition Rule
Probability that either two events occur (no need to be disjoint) is found by
Rule 7: General Multiplication Rule
Probability that both of two events occurs, without requiring they be independent is found by
Independent and Disjoint
A and B are independent if
because the occcurence of A does not affect the occurrence of B.
Howeverm they are NOT disjoint events: two events are only disjoint if only one of the two events can occur - i.e.
tossing a coin.
Joint, Marginal, and Conditional Probability
Joint probabilities give the probability of two events occurring together. Events can be placed in a contingency
table. In this table, the marginal probability is found by looking at only the totals in the margins. Each row or
column shares a conditional distribution.
describes the "probability of B given A."
Random Variables
Variables based on the outcome of a random event. If you can list all the possible outcomes, the random variable
is the discrete random variable. If it can take on any value between two values in an interval, it is a continuous
random variable.
Expected Value
Randomness and Probability
September 20, 2017
4:32 PM
Statistics Page 1
Document Summary
The theoretical probability of event a can be computed by whenever the outcomes ae equally likely. If the probability of an event occurring is the event. Disjoint or mutually exclusive events have no common outcomes. Adding probabilities of disjoint events gets the probability that either occur. The probability of a set must be 1, as in , where represents the set of all possible outcomes and is the where is the complement of . For two independent events a and b, the probability that both occur is. A and b are independent if because the occcurence of a does not affect the occurrence of b. Howeverm they are not disjoint events: two events are only disjoint if only one of the two events can occur - i. e. tossing a coin. Probability that both of two events occurs, without requiring they be independent is found by. Probability that either two events occur (no need to be disjoint) is found by.
