3 Discrete Probability Distribution

Question 1

Discrete Random Variable

Answer 1

Question 2

Discrete Probability Distribution Ex1

Answer 2

Question 3

Discrete Probability Distribution Ex2

Answer 3

Question 4

Discrete Probability Distribution Ex3

Answer 4

Question 5

Cumulative Distribution Function

Answer 5

Question 6

Cumulative Discrete Distribution Function ex1

Answer 6

Question 7

How to find the mean and variance for a discrete random variable

Answer 7

Question 8

Finding mean and variance of a discrete random variable ex1

Answer 8

Question 9

Finding mean and variance of a discrete random variable ex2

Answer 9

Question 10

What happens when you add/subtract a constant vs multiply/divide to a random variable?

Answer 10

Question 11

Transformation of random variable ex1

Answer 11

Question 12

What will happen if you add X + Y if both are random variables?

Answer 12

Question 13

Transformation of random variable ex2

Answer 13

Question 14

What is a discrete uniform distribution

Answer 14

Is the simplest of all probability distributions and is where the random variable assumes each of its values with equal probability. A random variable X has a discrete uniform distribution if each of the n values in its range has equal probability

Question 15

How do you find the mean and variance of a discrete uniform distribution?

Answer 15

E(x) = (b+a)/2

Variance = ( (b-a+1)^2 - 1 )/ 12

Where b= max and a = min

Question 16

Discrete Uniform Distribution Example

Answer 16

Question 17

What is a Bernoulli Random Variable?
Give the following:
1.) probability mass function notation
2.) mean
3.) variance

Answer 17

Question 18

Bernoulli Random Variable ex1:

1.)Give me the probability mass function
2.) expected value
3.)variance

Answer 18

Question 19

What is the Binomial Random Variable?
Find the following:

1.) Assumptions
2.) Probability Mass Function
3.) Expected Value
4.) Variance

Answer 19

Question 20

Binomial Random Variable ex1

Answer 20

Question 21

Binomial Random Variable ex2

Answer 21

Question 22

What is a Geometric Random Variable?
Give me the following:
1.) Assumptions
2.) Expected Value
3.) Variance
4.) probability density function
5.) cumulative density function

Answer 22

Question 23

Geometric Random Variable ex1

Answer 23

Question 24

Geometric Random Variable ex2

Answer 24

Question 25

What is a **Negative Binomial Distribution**? 1.) assumptions 2.) examples of when to use it 3.) expected value 4.) variance 5.) Probability density function

Answer 25

It is the probability of the math success happens on the xth trial. Assumptions: 1.) Binary(success or failure) 2.) Independent( one trial does not effect another) 3.) Number of trials until k success occur( desired # successes determined in advance) 4.) Probability of success is the same for each trial

Question 26

Negative Binomial Distribution ex1

Answer 26

Question 27

Negative Binomial Distribution ex2

Answer 27

Question 28

Negative Binomial Distribution ex3

Answer 28

Question 29

What is the **Hypergeometric Distribution**? 1.) assumptions 2.) expected value 3.) variance 4.) probability density function 5.) example when to use it.

Answer 29

Question 30

Hypergeometric Distribution ex1

Answer 30

Question 31

Hypergeometric Distribution ex2

Answer 31

Question 32

Hypergeometric Distribution ex3

Answer 32

Question 33

What is the **Poisson Distribution**? 1.) assumptions 2.) expected value 3.) variance 4.) probability density function

Answer 33

Question 34

Poisson Distribution ex1

Answer 34

Question 35

Poisson Distribution ex2

Answer 35

Question 36

Poisson Distribution ex3

Answer 36