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MathidiaMathematics Academy
Statistical distributions
Lesson 51 of 75
Introduction

Discrete random variables

Objective. Construct and interpret probability distributions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A discrete random variable is a quantity whose numerical outcomes from a random process can be listed, each with its own probability. You build a probability distribution by listing every possible value and assigning P(X=x) to each, and these probabilities must sum to 1. For example, rolling a fair die gives X with P(X=x)=1/6 for x=1,2,...,6. You can also find probabilities of events like P(X>4) by adding the relevant individual probabilities, and use the distribution to answer questions about likelihood of ranges of outcomes.

Worked example

A discrete random variable X has P(X=1)=0.2, P(X=2)=0.3, P(X=3)=k. Find k.

1 … 0.2
Illustrated card showing 1 … 0.2
  1. 1Probabilities of a discrete random variable sum to 1
  2. 20.2+0.3+k=1
  3. 30.5+k=1
  4. 4k=0.5

Answer: 0.5

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Practice

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Common mistake. Students forget to check that probabilities sum to 1, accepting a table where values total 0.9 or 1.1. Always add every listed probability first; if it is not 1, find the missing value using ΣP(X=x)=1.

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