Summary
Highlights
A random variable is a function that associates a real number with each element in the sample space, which is a collection of possible outcomes of a random experiment. Essentially, it's a numerical quantity determined by chance from the outcomes of an experiment.
Examples include the number of heads when tossing a coin, the sum of two numbers when rolling two dice, or the number of times a spinner stops at a specific number.
The steps involve assigning letters to represent outcomes, determining the sample space, and then counting the number of the random variable based on the defined event.
In an experiment tossing three coins, if X represents the number of heads, the possible values for X are 0, 1, 2, and 3. This is found by listing all possible outcomes (e.g., HHH, HHT, HTH, THH, HTT, THT, TTH, TTT) and counting the heads in each.
If two people are tested for COVID-19 and X represents the number of infected persons, with P for positive and N for negative, the possible outcomes are PP, PN, NP, NN. The values for X (infected persons) would be 0, 1, and 2.
Discrete random variables can only take a finite number of distinct, exact values, represented by non-negative whole numbers (obtained by counting). Continuous random variables can assume an infinite number of values within an interval, including fractions and decimals (often results of measurement).
Examples of discrete variables include the number of patients per day and the number of male athletes (because they are counted). Examples of continuous variables include the temperature of COVID-19 patients and the amount of sugar in coffee (because these are measured).