Random variables can be either discrete or continuous.
The mean (expected value) of a random variable represents the long-term average outcome.
The variance and standard deviation measure the spread or dispersion of the values of a random variable.
In comparing two independent population means, we often assume that the underlying data for each sample are realizations of independent random variables.
The difference between two population means can be modeled as a new random variable with its own mean and variance.
Review Questions
What is the difference between a discrete and continuous random variable?
How do you calculate the expected value of a random variable?
Why is it important to consider the variance when comparing two independent population means?
Related terms
Discrete Random Variable: A type of random variable that has specific, countable outcomes, such as rolling a die.
Continuous Random Variable: A type of random variable that can take any value within a given range, such as the height of individuals.
Expected Value: $E[X]$ represents the mean or average value expected from repeated trials of an experiment involving the random variable $X$.