A probability distribution is a formula describing the way a random variable behaves, or our assumptions about the potential values of an unknown parameter. The TI-83 series calculators include a variety of commands that describe very common distributions (although you can calculate the probabilities directly, they often have complicated formulas, and it is faster to use these commands instead).
For the continuous distributions, …pdf( gives the probability density function (mainly useful for graphing), and …cdf( gives the actual probability of a result occurring in an interval. For the discrete distributions, …pdf( gives the probability for a single value, and …cdf( gives the probability for all values up to some limit.
When calculating confidence intervals and significance tests, using these functions approaches the "using a table" experience more closely, and gives you a better idea of what's going on; however, the appropriate Test or Interval command, if available, will be easier and faster (as well as smaller, if in a program) to use.
There are also four "shade" commands available: rather than just calculating a value, they also draw the curve of the probability density function on the graph screen, and shade in the area that corresponds to the desired probability.
The following probability distribution commands are available: