Probability Distributions
As (perhaps) the name suggests, a Probability Distribution is a collection
(distribution) of the probabilities of events occurring.
o Better stated, a collection of the events (outcomes) and their probabilities.
Discrete Random V

Probability Distribution Rules:
1.Probabilities cannot be negative, nor can they be greater than one
2.The outcomes that can occur cannot overlap - Mutually Exclusive
3.All the outcomes must be accounted for - Collectively Exhaustive
Mutually Exclusive:
A

Questions & Answers to Proportions
o What proportion of the drivers failed the test
o P (F)
=
.23
o What percentage of the drivers who Passed (77) the test are Drunk (5)
o P (D | P) = 5/77= .065
o What proportion of the drivers who Failed (23) the test we

Rolling Dice Example - Conditional Probability
If we are to roll 2 dice and roll a 1 with the first one, what is the probability we roll a
1 with the second one?
o Is it 1/5 or maybe 0/5? or 0/6? or 1/6
It IS 1/6!
But thats different from the Men and Ladi

Probability Distribution
The MEAN of a Probability Distribution is the sum of (each value times its respective
probability) (x * P(x )
The STANDARD DEVIATION of a Probability Distribution is The Square root of:
the sum of [(each value minus the MEAN) squa

The Central Limit Theorem
Assume you are to flip coins.
Heads = 1
Tails = 0
If you toss a coin once, what would the AVERAGE be: either 0 or 1.
If you toss a coin twice, what could the AVERAGE be: it could be zero (2 tails) with a
probability of .25, it co

Testing in Decision Making:
o What percentage of the drivers who Passed the test are Drunk?
o P (D | P)
=
?
o What proportion of the drivers failed the test
o P (F)
=
?
o What proportion of the drivers who Failed the test were Sober
o P (S | F)
=
?
Other

Statistic Definitions
Data - numeric information we collect through measurement, observations, or counts.
Experiment act of obtaining data
A simulation uses a mathematical model to reproduce conditions of an experiment
Census is a count or measurement of

Standard Deviation in Probability Distribution
Why the confusing new way?
Using the old method, to calculate the mean we would need to list all (123)
numbers, add them up and divide by 123.
There are 33 of the number 19, 12 of the number 20 Wouldnt you ju

Probability of Success
o Using the newly discovered Binomial formula, find the Probability Mary gets 4 As, 3As
and 2 As
o P(4) =5*.8*.8*.8*.8*.2 = .4096
o P(3) =10*.8*.8*.8*.2*.2 = .2048
o P(2) =10*.8*.8*.2*.2*.2 = .0512
Binomial Distribution Tables
o Int