Types of distributions

Annotations:

• These distributions are used for discrete data

1. Discrete random variable
   1. Often presented as a frequency chart or bar graph. We are able to find the expected value and variance.
      1. Could be a rectangular distribution- bars the same height
2. Poisson distribution
   1. Random discrete events over a continuous interval. Usually presented as a rate or average per interval.
      1. Conditions: *events or happenings must occur at random *each event or happening must be independent of any others *events cannot occur simultaneously *the rate at which an event occurs is constant
3. Binomial distribution
   1. Set number of trials with the same probability in each trial. Only two possible outcomes.
      1. Conditions: *the number of trials must be fixed *each trial must result in either success of failure *each trial must be independent of the others *the probability of success at each trial must be the same
4. Normal distribution

Annotations:

• These distributions are used for continuous data

1. With a continuity correction we can sometimes model a discrete dist with a normal dist
   1. Bell shaped curve. A measures quantity in a measured interval. Often a good representation for naturally occurring measurement data.
      1. Conditions: *it is a bell shaped curve symmetrical about the mean *the area under the curve is one *there will be about six standard deviation over the range of the dist
2. Uniform distribution
   1. Where we know maximum and minimum values and we have no basis for assuming a particular shape to the dist. Sometimes called Continuous Rectangular Distribution.
3. Triangular distribution
   1. Where we know maximum, minimum and mode values and we assume a linear increase from minimum to mode and then down to the maximum.