# How to prepare for Midterm II and other comments – MATH 4510/5510

### General Information and instructions for the exam

We will be doing Midterm II on April 14th, during time class. You will need to be online on our Zoom meeting as you do the exam.

### General Content

The exam will cover the following chapters of our textbook:

1. Chapter 3: Conditional Probability, Bayes Formulas, Multiplication Rule, Independence of Events;
2. Chapter 4: Random Variables, Expected Value, Variance and Standard Deviation, Chebyshev’s Inequality, Probability distribution: Binomial, Poisson, Geometric;

### Important things you must know for Midterm II

1. You must know how to solve problems involving conditional probability and independence of events. In this case, tools like Multiplication Rule and Bayes’ Formulas are really important;
2. You must know the formal definition of concepts like: Independence of Events, Random Variable, Probability Distributions, Cumulative distribution function. You also must know how to compute Expected Value, Variance and Standard Deviation;
3. You must know how to use information given by expectation and variance to provide estimates on the probability of deviations from the mean in general contexts. Here Chebyshev’s Inequality is vital!
4. You must be able to identify when a given situation can be modeled by some known probability distribution.

### How to prepare for Midterm II?

1. For Chapter 3, the hint is to go through practical problems involving conditional probabilities. The problems suggested in the assignments are a good start; Also give the problems from Chapter 3 a try!
2. For Chapter 4, you can go through all the slides and read the concepts there. In the slides you also find some use cases of expected value and variances and how to compute them.
3. Give special attention to the Chebyshev’s Inequality. It is crucial that you know how to use it. So, you must know its statement and when to use it. The extra question on Homework #7 is a good way to know how to use Chebyshev’s Inequality and a good prototype problem.