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Notes 6
1
PROBABILITY and RA&DOM VARIABLES
Random Process
:
A process is said to be
random
if the outcomes of independent
trials
are
uncertain, but a pattern of outcomes emerges in the long run after very
many trials.
: Trials are “independent” if the outcome of one trial does not influence the outcome of any
other trial.
Example
:
The result of any single coin toss is random.
However, the result over many tosses is
predictable, as long as the trials are
independent
(i.e. the outcome of the next coin
toss has nothing to do with the previous tosses).
The red line represents starting with a tail on the 1
st
toss; the black line represents starting with
a head on the head on the 1
st
toss.
Sample Space (S)
: This is a set of all
possible outcomes in a random process.
Example
: (1)
A coin toss has two possible outcomes. Therefore the sample space for this
random process is S = {head, tail}.
(2)
Rolling a die has 6 possible outcomes.
S = {1,2,3,4,5,6}
(3)
The sum of the numbers that show up when a die is rolled twice.
S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
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View Full Document Notes 6
2
Event
:
An event is a subset of the outcomes from the sample space.
Note
: Events are usually written as verbal descriptions labeled A, B, C etc.
..
Examples
:
A = {Getting a sum less than 7 when two die is rolled twice} = {2, 3, 4, 5, 6}
B = {Getting at least one tail when two coins are tossed} = {HT, TH, TT}
E= {Rolling an even number on one roll of a die}.
E = {2, 4, 6}
Probability
:
The probability of an outcome of a random process is the proportion of times that
the outcome occurs in very many independent trials.
(i.e. in the long run)
**Recall that relative frequency is proportion or percentage.
Therefore, you can think of
probability as a "longrun" relative frequency or longrun proportion.
**Probabilities are always fractions or decimals indicating the portion or percent of the time that
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This note was uploaded on 04/02/2012 for the course STA 2023 taught by Professor Bateh during the Spring '08 term at Florida State College.
 Spring '08
 BATEH
 Statistics, Probability

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