2 min read•june 3, 2020

Kanya Shah

Focus on the big picture in terms of what context the variables exist in.

A **random variable **takes numerical values that describe the outcomes of a chance process. The **probability distribution** of a random variable gives its possible values and their probabilities. To assign labels to random variables, we use capital letters (X or Y).

A **continuous random variable** can take any value in an interval on the number line so this includes whole numbers and decimals for value of X. Generally, you use a density curve to find the probability of a continuous variable and the probability usually applies to an interval rather than individual values.

A **discrete random variable **X takes a fixed set of possible values with gaps between them (cannot include decimals so, whole numbers only). *For a probability distribution to be valid, each probability must be between 0 and 1, inclusive. Also, the sum of the probabilities must add to 1.

When calculating probability for discrete random variables, always think about whether you should include the boundary value in your calculations. *Make sure you understand how to calculate the probability of a discrete random variable given P(Xn) and P(X=n). *The wording is usually confusing so draw yourself a mini probability distribution chart to figure out whether you should/shouldn’t include the boundary value. This will help you when there are phrases like **at least, no more than, greater than,** etc.

Value | x1 | x2 | x3 | x4 |

Probability | p1 | p2 | p3 | p4 |

You need to know how to represent a discrete random variable as a histogram or in a table. For the histogram, use the discrete random variable as the x axis values and the probabilities for the y axis.

When describing the shape of a discrete random variable, talk about whether the graph is roughly symmetric, double/single peaked, and right/left skewed. Don’t forget to mention the center (mean) and measure of variability (standard deviation). These interpretations will allow you to make conclusions.

🎥**Watch: AP Stats - ****Probability: Random Variables, Binomial/Geometric Distributions**

Sign up now for instant access to 2 amazing downloads to help you get a 5

Browse Study Guides By Unit

📆

Big Reviews: Finals & Exam Prep

✏️

Blogs

✍️

Free Response Questions (FRQs)

👆

Unit 1: Exploring One-Variable Data

✌️

Unit 2: Exploring Two-Variable Data

🔎

Unit 3: Collecting Data

🎲

Unit 4: Probability, Random Variables, and Probability Distributions

📊

Unit 5: Sampling Distributions

⚖️

Unit 6: Inference for Categorical Data: Proportions

😼

Unit 7: Inference for Qualitative Data: Means

✳️

Unit 8: Inference for Categorical Data: Chi-Square

📈

Unit 9: Inference for Quantitative Data: Slopes

Practice your typing skills while reading Introduction to Random Variables and Probability Distributions

Start GameTake this quiz for a progress check on what you’ve learned this year and get a personalized study plan to grab that 5!

START QUIZStudying with Hours = the ultimate focus mode

Start a free study session