# 5: Continuous Random Variables

- Page ID
- 503

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A random variable is called *continuous* if its set of possible values contains a whole interval of decimal numbers. In this chapter we investigate such random variables.

- 5.1: Continuous Random Variables
- For a discrete random variable X the probability that X assumes one of its possible values on a single trial of the experiment makes good sense. This is not the case for a continuous random variable. With continuous random variables one is concerned not with the event that the variable assumes a single particular value, but with the event that the random variable assumes a value in a particular interval.

- 5.2: The Standard Normal Distribution
- A standard normal random variable \(Z\) is a normally distributed random variable with mean \(\mu =0\) and standard deviation \(\sigma =1\).

- 5.3: Probability Computations for General Normal Random Variables
- Probabilities for a general normal random variable are computed after converting \(x\)-values to \(z\)-scores.

- 5.4: Areas of Tails of Distributions
- The left tail of a density curve y=f(x) of a continuous random variable X cut off by a value x* of X is the region under the curve that is to the left of x*. The right tail cut off by x* is defined similarly.

- 5.E: Continuous Random Variables (Exercises)
- hese are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang.