Continuous random variable

Definition

A continuous random variable is a variable that can take an infinite number of possible values within a given range. It is often used to model quantities that are measured, rather than counted.

5 Must Know Facts For Your Next Test

1. Continuous random variables have probability density functions (PDFs) instead of probability mass functions (PMFs).
2. The area under the PDF curve over an interval gives the probability that the random variable falls within that interval.
3. The cumulative distribution function (CDF) represents the probability that a continuous random variable is less than or equal to a certain value.
4. For exponential distributions, the PDF is given by $f(x; \lambda) = \lambda e^{-\lambda x}$ for $x \geq 0$, where $\lambda$ is the rate parameter.
5. The mean of an exponential distribution is $1/\lambda$, and its variance is $1/\lambda^2$.

Review Questions

Related terms

Probability Density Function (PDF):

A function that describes the likelihood of a continuous random variable taking on various values.

Cumulative Distribution Function (CDF):

A function representing the probability that a continuous random variable is less than or equal to a certain value.

Exponential Distribution:

\text{A type of continuous distribution often used to model time until an event occurs, characterized by its rate parameter } \lambda.