Random Variables A random variable is a rule that assigns exactly one value to each point in a sample space for an experiment. A random variable can be classified as being either discrete or continuous depending on the numerical values it assumes. A discrete random variable may assume either a finite number of values or an infinite sequence of values. A continuous random variable may assume any numerical value in an interval or collection of intervals.

Random Variables QuestionRandom Variable x Type Family x = Number of dependents in Discrete size family reported on tax return Distance from x = Distance in miles fromContinuous home to store home to the store site Own dog x = 1 if own no pet; Discrete or cat = 2 if own dog(s) only; = 3 if own cat(s) only; = 4 if own dog(s) and cat(s)

Probability Distributions The probability distribution for a random variable describes how probabilities are distributed over the values of the random variable. The probability distribution is defined by a probability function which provides the probability for each value of the random variable.

Continuous Probability Distributions A continuous random variable can assume any value in an interval on the real line or in a collection of intervals. It is not possible to talk about the probability of the random variable assuming a particular value. Instead, we talk about the probability of the random variable assuming a value within a given interval.

The probability of the random variable assuming a value within some given interval from x 1 to x 2 is defined to be the area under the graph of the probability density function between x 1 and x 2. Continuous Probability Distributions

Probability Density Function For a continuous random variable X, a probability density function is a function such that (1) (2) (3)

Example

Does it Qualify?

Finding Value of k…

Using CAS

More Complicated

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More CAS…

Statistics using PDF…

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