Week 26th: April 5th - April 9th (Week A)
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
Week 27th: April 12th - April 16th (Week B)
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
Week 28th: April 26th - April 30th (Week C)
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