4 Continous Probability Distribution

Question 1

Describe a Continuous Random Variable

Answer 1

Question 2

Continuous Random Variable ex1

Answer 2

Question 3

Describe the Cumulative Density Function for a continuous variable.

Answer 3

Question 4

Cumulative Density Function ex1

Answer 4

Question 5

Cumulative Density Function ex2

Answer 5

Question 6

Cumulative Density Function ex3

Answer 6

Question 7

Describe the Mean and Variance of a continuous Random Variable

1.) Expected Value
2.) Variance
3.) Properties and expectation and variance

Answer 7

Properties
1.) E(aX+b) = aE(x) + b
2.) E(X +- Y) = E(X) +- E(Y)
3.)Var(aX + b) = a^2Var(X) + 0
4.) E(XY) = E(X)E(Y) (if X and Y are independent)
5.) Var(X + Y) = Var(X) + Var(Y) (if X and Y are independent)

Question 8

Mean and Variance of a continuous Random Variable
(Example 1)

Answer 8

Question 9

Mean and Variance of a continuous Random Variable
(Example 2)

Answer 9

Question 10

Describe the Continuous Uniform Distribution
1.) probability density function
2.) expected value
3.) variance

Answer 10

Question 11

Continuous Uniform Distribution ex1

Answer 11

Question 12

Continuous Uniform Distribution ex2

Answer 12

Question 13

For a binomial distribution, when is the distribution approximately normal?

Answer 13

1.) np > 5
2.) n(1-p) > 5

Question 14

For a Poisson distribution, when is the distribution approximately normal?

Answer 14

1.) mean >5

Question 15

For a hypergeometric distribution, when is the distribution approximately normal?

Answer 15

1) n/N < 0.1

Question 16

approximately normal ex1

Answer 16

Question 17

approximately normal ex2

Answer 17

Question 18

approximately normal ex3

Answer 18

Question 19

Describe the gamma distribution?
1.) probability density function
2.) expected value
3.) variance
4.) what is the gamma and exponential distribution used for?

Answer 19

Question 20

Gamma Distribution ex1

Answer 20

Question 21

Gamma Distribution ex2

Answer 21

Question 22

What are the special cases of the Gamma Distribution?

Answer 22

Question 23

Describe the Exponential Distribution
1.) Expected Value
2.) Variance
3.) Probability Density Function

Answer 23

Question 24

When would you is a exponential distribution vs Gamma Distribution vs Poisson? Give an example

Answer 24

Question 25

Exponential Distribution ex1

Answer 25

Question 26

Exponential Distribution ex2

Answer 26

Question 27

Exponential Distribution ex3

Answer 27

Question 28

Describe the Weibull Distribution
1.) probability density function
2.) expected value
3.) variance
4.) code

Answer 28

Question 29

Weibull Distribution ex1

Answer 29

Question 30

Describe the Lognormal Distribution and when to use it.
1.) Probability density function
2.) expected value
3.) variance

Answer 30

Question 31

Lognormal Distribution ex1

Answer 31

Question 32

Lognormal Distribution ex2

Answer 32