Discrete Probability Distributions

Question 1

What is Binomial Distribution?

Answer 1

A frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success

Question 2

What is a sample space?

Answer 2

The range of values of a random variable.

Question 3

What outcomes are usually associated with Binomial Distribution?

Answer 3

• success, failure
• yes, no
• presence absence

Question 4

What is a Discrete Probability Distribution?

Answer 4

• A discrete distribution describes the probability of occurrence of each value of a discrete random variable. A discrete random variable is a random variable that has countable values, such as, how many times you can roll a six with two dice

Question 5

What is the equation for Discrete Probability Distribution?

Answer 5

https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing

Question 6

What is the Symbol for the population mean?

Answer 6

= μ, this symbol, when used in the discrete population distribution is known as “np”
- “np” means the number of trials multiplied by the probability of a success

Question 7

What is the Symbol for the population variance?

Answer 7

= npq

- This means the sum of each value minus the expected value(the mean), squared by its associated probability

Question 8

What is the symbol for the population Standard deviation?

Answer 8

= √(npq)

Question 9

What is the Symbol for the Binomial Prob. Distribution?

Answer 9

= B(n,p)

Question 10

What is a Continuous Probability Distribution?

Answer 10

• A continuous distribution describes the probabilities of the possible values of a continuous random variable. A continuous random variable is a random variable with a set of possible values (known as the range) that is infinite and uncountable

Question 11

What is a cumulative binomial probability?

Answer 11

• We can ask a question like: “What is the probability of getting 5 or less heads, when flipping a coin ten times?” This is a cumulative binomial probability. We use the distribution function to get an answer.

Question 12

Give an example of a Cumulative Binomial Distribution Table.

Answer 12

https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing

Question 13

Give an example of a Cumulative Binomial Distribution Graph.

Answer 13

https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing

Question 14

What is the first criteria that a Binomial distributions data has to meet?

Answer 14

• To be classified as binomial, there are only two options for a result: Success or Failure

Question 15

What is the 2nd criteria that a Binomial distributions data has to meet?

Answer 15

• A binomial distribution assumes a set number of trials or a set number of repeating experiments

Question 16

What is the 3rd criteria that a Binomial distributions data has to meet?

Answer 16

• In a binomial distribution, the probability of success + the probability of failure must equal 1

Question 17

What is the 4th criteria that a binomial distributions data has to meet?

Answer 17

• Nothing that happens in any one trial will affect the results of the next trial. eg. when you flip a coin, the result you get won’t affect which side you get the next time you flip a coin

Question 18

Why don’t we calculate the probability of a success or failure in statistics?

Answer 18

• The calculations are time consuming and prone to calculation error.
• We look up these probabilities using a binomial table.

Question 19

What is a binomial table?

Answer 19

• A binomial table is designed for situations where there are only two possible outcomes.
• It allows us to quickly and efficiently find the probability of a success or failure for a particular experiment

Question 20

Give an example of a binomial table.

Answer 20

https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing

Question 21

What happens when most of the probability is on the left hand side of the binomial table?

Answer 21

• The graph or data in general will be skewed to the right
• If most of the data in the binomial table is on the right hand of the table then the graph or data will be skewed to the left

Question 22

What happens when the probability of success is equal on both sides of the binomial table?

Answer 22

This means that the graph, or data in general, will be symmetrically distributed, meaning that it is equal on both sides.

Question 23

What are unusual or extreme events in probability?

Answer 23

• Events whose probability is less than 5%

- Generally we are referring to what is referred to as tail probabilities

Question 24

Give an example of a tail probability.

Answer 24

https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing

Question 25

Why are there gaps between the bars in a discrete probability bar graph?

Answer 25

• The gaps between the bars are not interpret-able as data, because discrete data is not continuous, e.g. you can’t have 2.4 people.

Question 26

Why do you have to minus all the previous values from other trials when using a binomial table?

Answer 26

• The binomial table gives you a cumulative probability. That is, if you look up 2 on the table, you are looking up the probability of having an event occurring 2 times or less (e.g. 0, or 1, or 2).

Question 27

What is the first step in using a binomial table?

Answer 27

• First you need to pick the table that has the same number of experiments as yours.

Question 28

What is the 2nd step in using a binomial table?

Answer 28

• You need to select the probability of the outcome. For the example of an unbiased coin, this would be 0.5 (p=0.5)

Question 29

What is the 3rd step in using a binomial table?

Answer 29

• You need to stipulate how many times your event happened. For example how many times you flipped a heads on a coin

Question 30

What is the 4th step of using a binomial table?

Answer 30

• The fourth step is lining up the data
• For example if you have 7 trials of flipping a coin, a probability outcome of 0.5 for flipping a heads and the event happened 4 times or less then you would line up the row for the probability outcome (0.5) with the number of times the event happened(4 or less) an this would give you the answer

Question 31

How can you work out the probability of individual events?

Answer 31

• By subtracting sequential probabilities.
• E.g. if we wanted to know the probability of tossing a coin 7 times and getting heads 4 times we would get the probability for 4 or less and subtract the probability of getting three or less from it.
• P(x=4) = p(x≤4) - p(x≤3).

Question 32

How do you find the probability of getting x or more outcomes?

Answer 32

• To do this, we just need to remember that the total cumulative probability is 1
• For example: P(9>x) = 1 - P(x≤8)

Question 33

Give an example of finding the probability of getting x or more outcomes.

Answer 33

• What is the probability of tossing an unbiased coin 10 times and getting 9 or more heads?
• If the probability of 10 or less is 1 then we can subtract the profitability of getting 8 or less from 1 and we will have our answer
• P(9≥x) = 1 – P(x≤8)
  = 1 – 0.989
  = 0.011
• This makes sense because it would be pretty unusual if we tossed a coin 10 times and got a head 9 or 10 times out of ten trials.