Probability Distributions
A probability distribution describes all possible outcomes of a random variable and the probability associated with each outcome.
What You Need to Know
Key Concept Diagram
A discrete random variable takes countable values; its distribution is shown in a probability table
The sum of all probabilities in any probability distribution must equal exactly 1
The expected value E(X) = Σ[x · P(X=x)] is the long-run average outcome of the random variable
The normal distribution is a continuous bell-shaped distribution defined by its mean and standard deviation
Key Vocabulary
Random Variable
A variable whose value is determined by the outcome of a random process
Expected Value
The theoretical long-run average of a random variable, calculated as the weighted mean of all outcomes
Uniform Distribution
A distribution where every outcome has an equal probability of occurring
Normal Distribution
A symmetric bell-shaped continuous distribution completely described by its mean and standard deviation
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A random variable X has outcomes 1, 2, 3 with probabilities 0.2, 0.5, 0.3 respectively. What is E(X)?
Question 2
If the probabilities for outcomes are 0.3, 0.4, and k, what is k?
Question 3
Which property is true of every valid probability distribution?
Key Concepts Summary
- ●A discrete random variable takes countable values; its distribution is shown in a probability table
- ●The sum of all probabilities in any probability distribution must equal exactly 1
- ●The expected value E(X) = Σ[x · P(X=x)] is the long-run average outcome of the random variable
- ●The normal distribution is a continuous bell-shaped distribution defined by its mean and standard deviation