Workshop 4 - Discrete Distributions

Question 1

Probability distribution

Answer 1

List of probabilities, one for each possible value of (said variable)
Sum of probabilities is 1
Capital letter denotes random variable
Lower case letter denotes particular value that the random variable takes
E.g. P(Y=y)

Question 2

When would you use nCr?

Answer 2

To find the number of ways of choosing r objects out of n.

E.g. from a class of 30 students, how many ways are there of choosing 10 students? 30C10

Question 3

Binomial distribution

Answer 3

Conducts experiment in which the outcome is either a “success or failure”
Repeat n times
Let X be the number of times we see a “success”

Outcome of each experiment is independent of all other experiments
Each experiment has same probability of being a success
N must be a positive whole number

Max value for binomial random variable is the number of trials

Question 4

Poisson distribution

Answer 4

Count number of occurrences of an event
During specified period of time
Or specified area in space

Each occurrence is independent of Poisson distributional other occurrences.
Only one event can happen at any given time.
Average number of events over this time period is constant.
Only one event can happen at any given point in space.
Average number of events in this area in space is constant.

No max value for Poisson random variable

Mean = variance