Discrete random variable and continuous random variable

[AToma4828]

What do we mean when we say that a discrete random variable can take on finite countable number of values ? like does that mean that we can't have any value which has a decimal part to it.

 

[David Harper CFA FRM]

Hi @AToma4828 A cumulative distribution function (CDF) which describes a random variable is a plot of probabilities on the Y axis (from 0 to 100%) against, on the X axis, the range (aka, support) of outcomes (possible values) of the random variable. If it's a fair die, the range is {1, 2, 3, 4, 5, 6} and the describing CDF is a discrete uniform distribution because we can count these outcomes. A fair coin has a range of {H, T} which are not numerical in value but we can count them. The outcomes (values on the X-axis) can be anything categorical, include non-numbers (e.g., text labels, country names, colors, animals, states, weekdays) or numbers with decimals, but it's discrete if we can count them. It's maybe non-rigorous, but if the plot is a barplot, then it's discrete! A good example of continuous (non-discrete) is any time process: if you plot time on the X-axis, although you could count each minute (or hour) etc, you'd never be able to actually count all the outcomes because there's always an outcome in between two other times. So you need a line for that! Hope that's helpful,