Cálculo Diferencial - Module 1. Probability
and statistics.
Alejandro Baruch Saucedo Esparza - A01400284
Lic. Saul Garcia
Probability and statistics
1.1Probability Basic Concepts
Deterministic Phenomenon: It can be
predicted exactly on the basis of obtainable
information
Random Phenomenon: It
fluctuates in such a way
that its value cannot be
predicted exactly with
obtainable information
Probability
Basic Concepts
Outcomes
Possible Results of the experiment
Sample Space
Set of all possible answers
event
Any subset of the
sample space
Experiments
Observation or measurement of
a random phenomenon
Odds
Compare the number of favorable
outcomes with number of
unfavorable outcomes.
Ex: To get 1 in dais. 1 to 5 favorable outcomes, 5 to one unfavorable, 1/6 probabilities
Probability Formulas
Theoretical Formula
Empirical Formula
Converting between probability and odds
Let E be an event If P(E)= a/b, then the
odds in favor of E is (b-a) If the odds in favor
of E are a to b, then P(E)=a/(a+b)
Properties of Probability
Let E be an event within the sample
space (S). That is E a subset of S then
the following properties hold
Probability of value
Impossible event
Certain event
Events Involving "NOT" and "OR"
Probability of the complement
Probability that on event E will
not occur (Not E) is equal to 1 minus the probability that will occur. P(not E)=1-P(E)
Addition rule of probability
If A and B are any two events then:
P(A or B)=P(A) + P(B) - P(A and B).
If A and B are mutually Exclusive
then: P(A or B)= P(A)+P(B)
Two events are mutually exclusive if
they have no outcomes in
common(can´t occur simultaneously)
Events Involving and
The probability of event B, Computed
on the assumption that event A has
happened, is called the conditional
probability of B given A and is denoted
P(A/B)
Conditional Probability formula (of B given A)
Multiplication rule of probability
Independent events
Two events are called independent events if the
knowledge about the occurrence of one of them
has no effect on the probability of the other one, that is, if
P(B/A)=P(B), or equivalently, P(A/B)=P(A). (applies in all cases)
P(A and B)=P(A)P(B)
Any two events
P(A and B)=P(A)P(B/A)
Venn Diagrams
Let A and B be any sets,
with U the universal set.