# Mochi does Maths!

## Ms Carolina's Math class

### Lesson 1 - Discrete random Variables

Period 1

In this lesson you will learn:

- to determine whether a random variable is discrete or continuous.

- to find the probability distribution for a random variable X using a table, a graph or as a function.

- to find the expected value (mean) and standard deviation (or variance) of a discrete random variable X.

Before class:

- Watch: Watch the video lesson on the introduction to random variables.

- Watch: Watch the video lesson on expectation for random variables.

- Read: Mathematics AA HL by Oxford, page 696-700

During class:

- Investigation 4: page 696-697

- Investigation 5: page 699

- Exercise 11D page 699

- Exercise 11E page 701.

### Lesson 2: Expectation and standard deviation of a linear function of a discrete random variable

Period 2

In this lesson you will learn:

- to find the probability distribution of a random variable Y, that is a linear function of a discrete random variable X (Y=aX+b).

- To find the expected value and variance of a random variable Y, that is a linear function of a discrete variable X (Y=aX+b).

Before class:

- Watch: watch the video lesson on expectation for linear combinations of one discrete random variable.

- Read: MAA HL by Oxford. page 701 - 705

During class:

- Investigation 6, page 701-702

- Exercise 11F, page 705

### Lesson 3: The binomial distribution

Period 1

In this lesson you will learn:

- To identify binomial experiments

- To calculate binomial probabilities.

- To find the probability distribution of a binomially distributed random variable X.

- To find the expected value and variance of a binomially distributed random variable X.

Before class:

- Watch: watch the video on the characteristics of a binomial experiment, how to calculate binomial probabilities, and how to find the expected value for a binomial random variable.

- Attempt to find an expression for the variance of a binomial distribution.

- Read: MAA HL by Oxford. page 712 - 717

During class:

- Investigation 7, page 713

- Investigation 8, page 716

- Exercise 11I, page 717

### Round up on Discrete random variables

Period 2

In this lesson you will learn:

- To find the median of a discrete random variable

- To find the quartiles of a discrete random variable

- To find the IQR of a discrete random variable

In this lesson you will practice:

- how to calculate probability values and expectation in problems around discrete random variables.

Before class:

- Please review the materials of Lessons 1-3. Please bring your calculator, as well as a device where you can see the textbook.

During class:

### Lesson 4 - Continuous random variables

Period 3

In this lesson you will learn:

- To identify continuous random variables

- To calculate continuous probabilities.

- To find the probability density function of a continuous random variable X.

- To find the expected value and variance of a continuous random variable X.

- To calculate probabilities using the cumulative distribution function.

Before class:

- Watch: watch the video on the characteristics of continuous random variable, how to calculate probabilities and expectation for this type of random variables.

- Read: MAA HL by Oxford. page 706 - 711

During class:

- Exercise 11G, page 708

- Exercise 11H, page 711-712

### Lesson 5: The normal distribution

Period 1

In this lesson you will learn:

- To identify the normal distribution

- To find normal probabilities

Before class:

- Watch: watch the video on the characteristics of the normal distribution.

- Read: MAA HL by Oxford. page 718 - 722

During class:

- Exercise 11J, page 722

### Lesson 6: The inverse normal distribution and the inverse normal distribution

Period 1

In this lesson you will learn:

- To standardize a normal distribution

- To associate normal variables to their corresponding z-scores

- To find the value of x, given P(X<x)

Before class:

- Watch: watch the video on the characteristics of the standard normal distribution.

- Watch: watch the video on the inverse normal distribution.

- Read: MAA HL by Oxford. page 723

During class:

- Exercise 11H, page 724