Lecture 3 - Ch 5 - Discrete Random Variables

We calculated the mean, variance and standard deviation for a set of data earlier. Those calculations are made on a finite set of data points (observations).

If, rather than data, we have an event that is described theoretically by a discrete random variable with possible values and the probability of each value, we can make similar calculations. The difference here is that in a set of data each observation is equal to the next. But in a random variable, we weigh the possible values by their respective probabilities.

Mean - Add up all the possible values but instead of dividing by the number of values, we multiply each by its probability.Variance and Standard Deviation - Std Dev is still the square root of the variance. But the variance is the sum of the squares of the difference between the data points and the mean times the probability of that data point.