4.7 Introduction to Random Variables and Probability Distributions

Part of Probability, Random Variables, and Probability Distributions in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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What is a Random Variable?

Random variable

Two types:

Discrete random variable — e.g., number of heads in 3 flips: X ∈ {0, 1, 2, 3}
Continuous random variable — e.g., height, weight, time

Probability distribution of a discrete random variable: A table (or formula) giving the probability for each possible value:

Value ${x}$	${P(X = x)}$
0	0.125
1	0.375
2	0.375
3	0.125

Requirements:

${0 \leq P(X = x) \leq 1}$ for all ${x}$
${\sum P(X = x) = 1}$

In this unit

12 lessons

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