# Normal and Exponential Probability Distributions - PowerPoint PPT Presentation

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## Normal and Exponential Probability Distributions

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### Normal and Exponential Probability Distributions Prof. Tom Willemain * * T.R. Willemain Analysis of dataset on MAU web site. Consider American Airlines flight 001 ... – PowerPoint PPT presentation

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Title: Normal and Exponential Probability Distributions

1
Normal and Exponential Probability Distributions
• Prof. Tom Willemain

2
Normal Distribution
• Also called Gaussian distribution

3
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4
Normal density curves
5
The standard normal distribution
6
Nonstandard normal distribution
7
Percentiles of normal distributions
8
Normal Probabilities and Percentiles in Minitab
9
In-Class Exercise
• X N(15, 22).
• Calculate the following
• P(X lt 16) P(X 16) ?
• 78th percentile of X ?

10
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11
Special Properties of Normal pdf
• If X1 and X2 are normal RVs, then X1X2 also has
a normal distribution.
• If X1 N(µ1, s12) and X2 N(µ2, s22) AND if
X1 and X2 are independent, then
• X1X2 N(µ1µ2, s12s22)
components are independent

12
Normal probability plot
This is an informal, graphical test. If the data
plot close to a straight line, we are safe in
assuming normality.
13
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14
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15
Random Normal Data in Minitab
16
plot confirms that Minitab generated Normal data
17
Exponential Distribution
18
The exponential distribution
19
Exponential density curves
20
Memoryless Property of Exponential
• Ex P X gt 100 X gt 90 PX gt 10, so its as
if time restarted at 90.
• This property is unique to the exponential and
makes certain analyses easy.
• We know that PX gt x exp(-?x) for all x 0
• So what is PX gt x X gt c (for any x gt c)?
• PX gt x AND X gt c/PX gt c
• PX gt x/PX gt c
• exp(-?x)/ exp(-?c) exp(-?x-c) QED

21
Exponential Distribution in Minitab
22
Exponential Probability Plot
23
In-Class Exercise
• The time before failure of an electronic black
box has an exponential distribution with mean
150 hours.
• Compute
• Plifetime is between 100 and 200 hours

24
In-Class Exercise
P100ltlifelt200 0.74-0.49 0.25
25
Demonstration of the Use ofRandom Numbers