Transcript Probability Distribution

Probability Distribution
The probability distribution for
a random variable is an
assignment of probability to
each of the possible values for
the variable
Probability Distributions
Discrete Probability Distributions
1.
2.
3.
4.
The
The
The
The
Uniform Distribution;
Binomial Distribution;
Hypergeometric Distribution; and
Poisson Distribution
Continuous Probability Distributions
1. The Uniform Distribution; and
2. The Normal Distribution
Mean of a Discrete
Probability Distribution
The mean of a discrete probability
distribution is also called the expected
value of the discrete random variable.
E( X ) 

XP( X )
where, E(X) = expected value of X
X = values of the random variable
P(X) = probability of each value of X
Standard Deviation of a Discrete
Probability Distribution
Standard Deviation of a discrete random
variable
2
 x  SQRT
  x  E ( x) P( x)
where, X = values of the random variable
E(X) = expected value of X
P(X) = probability of each value of X
The Binomial or Bernoulli Process
The experiment consists of n identical trials;
Each trial results in one of two outcome,
success or failure;
The probability of success on a single trial is
equal to p, and remains the same from trial to
trial. The probability of failure is ( 1 - p );
The trials are independent; and
The experimenter is interested in X, the number
of successes observed during the n trials.
Example: Taste Test; Coke Vs. Pepsi
Sample size (n) = 3, P(Coke is preferred) = 0.20
Simple
Event
e1
e2
e3
e4
e5
e6
e7
e8
Consumer
One Two Three
C
C
C
C
C
P
C
P
C
C
P
P
P
C
C
P
C
P
P
P
C
P
P
P
P(ei)_
___
(0.20)3
= 0.008
(0.20)2(0.80) = 0.032
(0.20)2(0.80) = 0.032
(0.20)(0.80)2 = 0.128
(0.20)2(0.80) = 0.032
(0.20)(0.80)2 = 0.128
(0.20)(0.80)2 = 0.128
(0.80)3
= 0.512
1.000
Probability Distribution
Coke Vs. Pepsi
_X_ ___ei___ _P(X)_
0
e8
0.512
1
e4,e6,e7 0.384
2
e2,e3,e5 0.096
3
e1
0.008
1.000