Let’s Summarize

• When we have a quantitative variable with outcomes that occur as a result of some random process (e.g., rolling a die, choosing a person at random), we call it a random variable.
• Continuous random variables can take any value in an interval and are often measurements. We use a density curve to assign probabilities to intervals of x-values. We use the area under the density curve to find probabilities.
• The probability of an event happening between two numbers [latex]a[/latex] and [latex]b[/latex] is written as [latex]P(a≤x≤b)[/latex].
• The total area under a continuous probability distribution function is 1.
• A uniform distribution is a type of continuous random variable, where all outcomes are equally likely on a given range of values. Areas of rectangles are used to calculate probabilities associated with uniform distributions.
• Exponential probability distributions often follow a decay model with higher probabilities happening for small values and lower probabilities happening for larger values. The Poisson distribution is an example of an exponential distribution.