Final answer:
A random variable is a numerical outcome of a probability experiment, with values that vary per experiment repetition. There are two types: discrete, which are countable, and continuous, which are uncountable and result from measurements. Random variables are denoted using uppercase letters, while their specific values are lowercase.
Step-by-step explanation:
A random variable (often abbreviated as RV) is a variable whose values are numerical outcomes of a probability experiment. The values that a random variable can take on vary with each repetition of an experiment. There are two main types of random variables: discrete random variables and continuous random variables.
Discrete random variables have countable values, which are typically obtained by counting. For example, if we let X denote the number of heads when flipping three coins, X could take on the values 0, 1, 2, or 3, since we are counting the number of heads.
Continuous random variables, on the other hand, have uncountable values, often resulting from measurements. An example would be the height of trees in a forest, where the variable X could take on any value within a range, representing various possible heights measured.
Random variables are denoted by uppercase Latin letters such as X, Y, Z, while specific values taken by these variables are denoted by lowercase letters x, y, z. The domain of a random variable, which is the set of all possible values it can take, can be numerical or expressed in words, depending on the context of the study or experiment.
Examples of Random Variables
- Discrete Random Variable: Let X be the number of red marbles in a jar containing one blue, one red, and one white marble. After drawing one marble, X can be 0 or 1.
- Continuous Random Variable: Let X be the temperature of a randomly selected day in June in a city. The value of X could be any real number representing the temperature.