# Science:MATH105 Probability/Lesson 1 DRV/1.01 Discrete Random Variables

*Note to MATH 105 instructors: I want to have a simple problem here that introduces the idea of probabilities as an area, and is appropriate for MATH 105 students. I'm not sure this one is a good problem, but I'd be happy to use another problem or modify this one to make it more applicable to MATH 105 students. Suggestions welcome!*

## Discrete vs Continuous Random Variables

*to go on the "About" page", or elsewhere*

In MATH 105, we deal with

- discrete random variables, and
- continuous random variables.

You will notice that certain definitions and concepts between them will be related.

These concepts are introduced assuming no prior knowledge of probability, but they are discussed with an assumption of integration. That is, probability is introduced as an application of of integration.

## Discrete Random Variables

In any experiment, only one **outcome** occurs. If we flip a coin, the outcome will be either "heads" (H) or "tails" (T). If the coin is a "fair" coin, it is equally likely that the coin will land as tails or heads.

We are often interested in quantifying the **probability** that a certain outcome occurs. Suppose we toss a fair coin tossed two times, and want to the probability that the coin will land as tails both times.

There are four possible outcomes:

HH HT TH TT

Because the coin is fair, each outcome is equally likely to occur.