Discrete outcomes can be counted - How many TVs in your house? By contrast, continuous outcomes are typically measured - How much do you weigh? Chapter 7 focuses on the probabilities of many discrete outcomes.
It's not much of a shortcut, but some exams will ask you to use the shortcut formula specifically, so I demonstrate it here using the same data from question 1c)
Time for the tabular approach to finding the expected value of x ( I use a table to keep track of my calculations). The order of operations comes into play here - Remember P.E.D.M.A.S. from high school math?
The binomial formula looks nasty, but it's easy to use once you learn how the different parts work. Your calculator will do most of the heavy work for you, and all you'll need are three numbers that will be given in the question: n, p, and x.
Test your understanding of Binomial Distributions - each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.
Knowing how to use the binomial tables is a MUST for the test! They can save you critical time compared with using the binomial formula. The tables however are not intuitive and so you'll first need to understand what kind of question the tables are designed to answer. Once that's clear, you can rework most binomial problems so that the table can solve them quickly.
More binomial, more probability questions, more work with the values on the binomial tables.
This is a typical binomial distribution exam question. It's a trick question - the binomial 'setting' changes with each new question (a, b, c..) - so I show you what needs to be done to handle that. Binomial tables are introduced here and I show how they can be used as a much needed shortcut through the typically long calculations that binomial questions require.
When a discrete variable has only TWO possible outcomes (per observation), then it is a Binomial variable. The calculations of probabilities, expected value and variance are all different from the ones we just covered (for discrete probability distributions). I walk you through a question here that covers all of the new methods introduced with binomial variables.
One more exam-style question before we get to the Binomial section of Chapter 7. This solution requires the use of the probability tree to find the probability distribution of x.