Probability Distributions Notes | EduRev

Created by: Yatin Trivedi

: Probability Distributions Notes | EduRev

 Page 1


Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Probability Distributions
Page 2


Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Probability Distributions
Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Objective Objective: derive a function (pdf/pmf) that can be used to
accurately predict outcomes of an experiment.
Probability Distributions
Page 3


Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Probability Distributions
Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Objective Objective: derive a function (pdf/pmf) that can be used to
accurately predict outcomes of an experiment.
Probability Distributions
So far…
f f ( (x x) ) = 1.5 = 1.5 – – 6( 6(x x - - 50) 50)
2 2
49.5 49.5 ? ? x x ? ? 50.5 50.5
40 /
40
1
x
e f(x)
?
?
?
?
?
?
?
?
?
? ?
?
? ? ? ?
?
3 0
14
8
3
0 2
64 64
15
x
x
x
x
f(x)
•
•
•
… etc
0 ? x
Probability Distributions
Page 4


Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Probability Distributions
Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Objective Objective: derive a function (pdf/pmf) that can be used to
accurately predict outcomes of an experiment.
Probability Distributions
So far…
f f ( (x x) ) = 1.5 = 1.5 – – 6( 6(x x - - 50) 50)
2 2
49.5 49.5 ? ? x x ? ? 50.5 50.5
40 /
40
1
x
e f(x)
?
?
?
?
?
?
?
?
?
? ?
?
? ? ? ?
?
3 0
14
8
3
0 2
64 64
15
x
x
x
x
f(x)
•
•
•
… etc
0 ? x
Probability Distributions
• Exponential
• Gamma
• Normal
• Uniform
• Bernoulli
• Binomial
• Geometric
• Negative binomial
Special Distributions
Discrete Continuous
Page 5


Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Probability Distributions
Probability as a modeling tool for prediction
e.g., 
• gaming odds
• part construction
• inventory modeling
Objective Objective: derive a function (pdf/pmf) that can be used to
accurately predict outcomes of an experiment.
Probability Distributions
So far…
f f ( (x x) ) = 1.5 = 1.5 – – 6( 6(x x - - 50) 50)
2 2
49.5 49.5 ? ? x x ? ? 50.5 50.5
40 /
40
1
x
e f(x)
?
?
?
?
?
?
?
?
?
? ?
?
? ? ? ?
?
3 0
14
8
3
0 2
64 64
15
x
x
x
x
f(x)
•
•
•
… etc
0 ? x
Probability Distributions
• Exponential
• Gamma
• Normal
• Uniform
• Bernoulli
• Binomial
• Geometric
• Negative binomial
Special Distributions
Discrete Continuous
The simplest random variable: either 1 or 0 either 1 or 0
Bernoulli Distribution
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