Random Variables and Normal Distribution

This set of flashcards covers the basics of random variables, normal distribution, and related statistical concepts.

What is a random variable?

A result of a chance event that can be measured or counted.

How are random variables represented?

Random variables are represented using capital letters.

What are the two types of random variables?

Discrete (countable, fixed number) and Continuous (measurable, can include decimal values).

Define sample space in the context of random variables.

The totality of all possible outcomes.

What does the normal distribution curve look like?

It is a bell-shaped curve that lies entirely above the horizontal axis.

Who is known for the normal distribution and what is another name for it?

Carl Friedrich Gauss; it is also known as Gaussian Distribution.

What are the parameters of a normal distribution?

It has two parameters: the mean (μ) and the standard deviation (σ).

What does the empirical rule state?

In a normal distribution, approximately 68% of values fall within one standard deviation, 95% within two, and 99.7% within three.

What is a Z-score?

A Z-score measures how many standard deviations a given value is above or below the mean.

What is the total area under a normal distribution curve?

The total area under the curve is equal to 1.