Random Variables and the Binomial Distribution

Name: Random Variables and the Binomial Distribution
Author: StemPy Lab

A basketball player takes ten free throws. How many will she score? You cannot say, but you can say how likely each count is. A random variable turns outcomes into numbers, and its distribution lists the chances. Find the mean and the variance of a random variable, then study repeated independent trials and the binomial distribution that describes them. The chapter ends with the normal approximation that A-Level and IB use for large trials. It covers the third part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Random variables and their distributions
A random variable turns each outcome of an experiment into a number. Its probability distribution lists the chance of each value. The mean $E(X)$ is the long-run average and the variance $\text{Var}(X)$ measures the spread. This lesson covers the table of a distribution, the mean and variance, the effect of $aX + b$ and the idea of a fair game.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 2about 25 min
Bernoulli trials and the binomial distribution
Many experiments repeat the same yes or no trial again and again: a free throw, a tossed coin, a tested part. When the trials are independent and each has the same chance of success, the number of successes follows the binomial distribution. This lesson gives the formula, the four conditions, and the mean $np$ and the variance $npq$ .
1 simulation1 practice question1 Python program4 problems
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Lesson 3about 25 min
Using the binomial model
The binomial formula answers many questions: at least one success, at most a few, the most likely count, and how many trials are needed. This lesson shows each of them, warns about sampling without replacement, and adds the normal approximation with its continuity correction that A-Level and AP use for large $n$ .
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
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Random Variables and the Binomial Distribution: Chapter Test

20 questions · 50 min

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Random Variables and the Binomial Distribution

Course outline (3 lessons)

Random variables and their distributions

Bernoulli trials and the binomial distribution

Using the binomial model

Test Your Learning

Your teacher

Discussion (0)