Probability distribution

1. 1

2. 2
4-1 Continuous Random Variables

3. 3
4-2 Probability Distributions and
Probability Density Functions
Definition

4. 4
4-2 Probability Distributions and
Probability Density Functions
Figure 4-2 Probability determined from the area
under f(x).

5. 5
4-2 Probability Distributions and
Probability Density Functions
Figure 4-3 Histogram approximates a probability
density function.

6. 6
Histograms

7. 7
4-2 Probability Distributions and
Probability Density Functions

8. 8
4-2 Probability Distributions and
Probability Density Functions
Example 4-2

9. 9
4-2 Probability Distributions and
Probability Density Functions
Figure 4-5 Probability density function for Example 4-2.

10. 10
4-2 Probability Distributions and
Probability Density Functions
Example 4-2 (continued)

11. 11
4-3 Cumulative Distribution Functions
Definition

12. 12
4-3 Cumulative Distribution Functions
Example 4-4

13. 13
4-3 Cumulative Distribution Functions
Figure 4-7 Cumulative distribution function for Example
4-4.

14. 14
4-4 Mean and Variance of a Continuous
Random Variable
Definition

15. 15
4-4 Mean and Variance of a Continuous
Random Variable
Example 4-6

16. 16
4-4 Mean and Variance of a Continuous
Random Variable
Expected Value of a Function of a Continuous
Random Variable

17. 17
4-4 Mean and Variance of a Continuous
Random Variable
Example 4-8

18. 18
4-5 Continuous Uniform Random
Variable
Definition

19. 19
4-5 Continuous Uniform Random
Variable
Figure 4-8 Continuous uniform probability density
function.

20. 20
4-5 Continuous Uniform Random
Variable
Mean and Variance

21. 21
4-5 Continuous Uniform Random
Variable
Example 4-9

22. 22
4-5 Continuous Uniform Random
Variable
Figure 4-9 Probability for Example 4-9.

23. 23
4-5 Continuous Uniform Random
Variable

24. 24
4-6 Normal Distribution
Definition

25. 25
4-6 Normal Distribution
Figure 4-10 Normal probability density functions for
selected values of the parameters  and 2
.

26. 26
4-6 Normal Distribution
Some useful results concerning the normal distribution

27. 27
4-6 Normal Distribution
Definition : Standard Normal

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4-6 Normal Distribution
Example 4-11
Figure 4-13 Standard normal probability density function.

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4-6 Normal Distribution
Standardizing

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4-6 Normal Distribution
Example 4-13

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4-6 Normal Distribution
Figure 4-15 Standardizing a normal random variable.

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4-6 Normal Distribution
To Calculate Probability

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4-6 Normal Distribution
Example 4-14

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4-6 Normal Distribution
Example 4-14 (continued)

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4-6 Normal Distribution
Example 4-14 (continued)
Figure 4-16 Determining the value of x to meet a specified
probability.

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4-7 Normal Approximation to the
Binomial and Poisson Distributions
• Under certain conditions, the normal
distribution can be used to approximate the
binomial distribution and the Poisson
distribution.

37. 37
4-7 Normal Approximation to the
Binomial and Poisson Distributions
Figure 4-19 Normal
approximation to the
binomial.

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4-7 Normal Approximation to the
Binomial and Poisson Distributions
Example 4-17

39. 39
4-7 Normal Approximation to the
Binomial and Poisson Distributions
Normal Approximation to the Binomial Distribution

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4-7 Normal Approximation to the
Binomial and Poisson Distributions
Example 4-18

41. 41
4-7 Normal Approximation to the
Binomial and Poisson Distributions
Figure 4-21 Conditions for approximating hypergeometric
and binomial probabilities.

42. 42
4-8 Exponential Distribution
Definition

43. 43
4-8 Exponential Distribution
Mean and Variance

44. 44
4-8 Exponential Distribution
Lack of Memory Property

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4-8 Exponential Distribution
Figure 4-24 Lack of memory property of an Exponential
distribution.

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4-11 Lognormal Distribution
with
^

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4-11 Lognormal Distribution
Figure 4-27 Lognormal probability density functions with  = 0
for selected values of 2
.

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4-11 Lognormal Distribution
Example 4-26

49. 49
4-11 Lognormal Distribution
Example 4-26 (continued)

50. 50
4-11 Lognormal Distribution
Example 4-26 (continued)