Probability Distributions
Random Variable A random variable x takes on a defined set of values with different probabilities. For example, if you roll a die, the outcome is random (not fixed) and there are 6 possible outcomes, each of which occur with probability one-sixth. For example, if you poll people about their voting preferences, the percentage of the sample that responds “Yes on Proposition 100” is a also a random variable (the percentage will be slightly differently every time you poll). Roughly, probability is how frequently we expect different outcomes to occur if we repeat the experiment over and over (“frequentist” view) Random variables can be discrete or continuous Discrete random variables have a countable number of outcomes Examples: Dead/alive, treatment/placebo, dice, counts, etc. Continuous random variables have an infinite continuum of possible values. Examples: blood pressure, weight, the speed of a car, the real numbers from 1 to 6.