Distributions

A univariate distribution is the distribution of a single variable. A multivariate distribution specifies the probabilities associated with a group of random variables. It is only meaningful when each variable in the group is in some way depenedent upon the other variables in the group.

A discrete uniform distribution is characterized by an equal probability for each outcome. An example is the results of a single die roll.

A confidence interval is a range of values around an expected outcome within which the actual outcome is expected to fall a specified percentage of the time. In other words, it is a range for which one can assert with a given probability that it will contain a parameter it intends to estimate.

Construction of a Confidence Interval

where

The Student's T-distrubution is a symmetrical distribution that is largely used to make inferences regarding the mean of a normal distribution whose variance is unnkown or when working with a small sample size.

The t-distrubtion is less peaked and has fatter tails than a standard normal distrubiton. This makes it a more conservative measure for constructing confidence intervals for the population mean.

Properties

The student's T-distrubtion is