Unit 4: Probability, Random Variables, and Probability Distributions

Probability rules, conditional probability, random variables, binomial and geometric distributions

This section contains 9 topics with 0 subtopics, 27 practice problems and 85 flashcards. Each topic includes comprehensive written notes, worked examples with detailed solutions, and interactive lessons for hands-on practice.

Topics Covered

• Basic Probability Rules — Apply addition and multiplication rules, and understand complements and mutually exclusive events.
• Conditional Probability — Calculate conditional probabilities using formulas and two-way tables.
• Independence — Test for independence using probability rules and understand its implications.
• Discrete Random Variables — Define discrete random variables, calculate expected value, variance, and standard deviation.
• Mean and Standard Deviation of a Discrete Random Variable — Compute and interpret the expected value, variance, and standard deviation of a discrete random variable from its probability distribution.
• Combining Random Variables (Sums and Differences) — Apply rules for the mean and variance of sums/differences of independent random variables, including linear transformations aX + b.
• Continuous Random Variables — Understand continuous random variables, probability density functions, and uniform distributions.
• Binomial Distribution — Apply the binomial distribution to count successes in fixed trials with conditions BINS.
• Geometric Distribution — Use the geometric distribution to model the number of trials until the first success.

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