Master the Fundamentals of Probability and Statistics

In this lecture, I will discuss about the concept of classical probability. A short note on the recap of probability tree is also included in this section. Please feel free to download the materials. Cheers! ;-)

In this lecture, I shall discuss about the concepts involving independent events and mutually exclusive events.

In this lecture, I will discuss about the concepts involving conditional probability and Bayes' theorem. Do take note that Bayes' Theorem is not in the GCE 'A' level syllabus.

Please download the notes before you listen to the lecture. Cheers! ;-)

In this lecture, I will discuss about solving of probability problems using permutations and combinations concepts. The brief notes are included in this section. Please feel free to download the file for your personal use. Also, please take note that due to a technical glitch of my microphone, you will notice there is a difference in the sound effect for the first 1min 25 sec as compared to the rest of the video. But it should not affect the overall quality of the lesson. I seek your kind understanding in this aspect. Thank you! Cheers! ;-)

In this lecture, we shall attempt to solve two probability questions. To optimize learning, I would suggest students to try the questions first before viewing the solutions. In addition, there is also a try-it-yourself problem which you can attempt during your free time. Cheers! ;-)

In this lecture, I shall discuss about the basic concepts involving discrete random variables. Cheers! ;-)

In this lecture, I will discuss about a popular distribution function for discrete random variables, called the Binomial Distribution. Please feel free to download the brief notes for the lesson. Cheers! ;-)

In this lecture, I will introduce a probability distribution for discrete random variables - the Geometric Distribution. ;-)

In this lecture, I will discuss a probability distribution for discrete random variables, where the concept is very similar to Binomial Distribution. ;-)

In this lecture, I will discuss about another probability distribution for discrete random variables - the Poisson Distribution! ;-)

In this lecture, I will discuss the solutions to 5 discrete random variables practice problems. For students who need more practices, I have also attached several problems in this section for further practices. Cheers!

In this lecture, I will discuss about several concepts involving continuous random variables. ;-)

In this lecture, I will introduce a probability distribution for continuous random variables - the Normal Distribution! The Normal distribution statistical table is attached in this section for your reference. In order to better understand how to calculate probability using the statistical table, please feel free to download and read the file "Examples using the Normal Distribution Function Table". In addition, there is a further practice problem which you can attempt to test your understanding. Cheers! ;-)

In this lecture, I will discuss about the concepts involving the use of the 'InvNorm' function of the graphic calculator as well as the use of the Normal distribution statistical table to determine unknown parameters.

In this lecture, I will discuss about the standardized Normal random variable Z and its concepts. Cheers! ;-)

In this lecture, I will discuss the concepts involving the linear combinations of Normal random variables. Cheers! ;-)

Dear student, this is a practice lesson for Normal Distribution. Please feel free to download the student version to try the problems before checking the solutions. There is no teaching video for this lecture. The Normal distribution statistical table is also attached in this lecture for your reference.

Thank you! Cheers! ;-)

In this lecture, I shall discuss the concepts involving cumulative distribution functions, and the relationship with probability density functions. Please feel free to download the lecture notes to read when you are going through the video. Cheers! ;-)

In this section, there is no teaching video. However, you are strongly encouraged to attempt the practice problems. Feel free to check your answers with the attached solutions. Cheers! ;-)

The Binomial distribution can be approximated well by Poisson when n is large and p is small with np < 10

In this lecture, I will discuss about the concepts involving the approximation of Binomial distribution to a Normal distribution. The technique of continuity correction will also be discussed. Cheers! ;-)

In this lecture, the attached materials will present information about the probability approximation from Poisson distribution to Normal distribution. Continuity correction is also applicable. Please feel free to download the notes for your reading. There is no lecture video at the moment for this topic. Cheers! ;-)

This is a problem-based practice lecture. There are a total of three questions, with each question covering the main concepts for each of the previous three topics on probability approximations. There is no teaching video at the moment. Cheers! ;-)

In this lecture, I shall discuss about the concepts involving sampling distribution and probability calculations, as well as the use of Central Limit Theorem. In addition, I have also included two pdf documents: "Proof of Expectation and Variance of Sample Mean" and "Sampling Methods notes" for your reading. The first document shows the proof of mean and variance of the sample mean and the second document is about the 4 main sampling methods.

Cheers! ;-)

In this lecture, I shall discuss about the Estimation Theory and the concepts involving unbiased estimation of population parameters.

In this lecture, I shall discuss about the concepts involving confidence intervals for population mean. The t-distribution for small samples will also be introduced. ;-)

In this lecture, there are four practice questions to help you get familiarized with the concepts of Sampling and Unbiased Estimation. You are strongly encouraged to try the questions first before checking the answers. The Normal distribution table and t-distribution table are attached in this lecture for your easy reference.

Cheers! ;-)

Dear students, in this lecture, I shall do a brief introduction to the main concepts of Hypothesis Testing. More examples can be found in subsequent lectures. Please feel free to download the pdf document when you are going through the lesson. Cheers! ;-)

In this lecture, I will show you an example of hypothesis testing when the population is normally distributed and variance is known. Cheers! ;-)

In this lecture, I shall discuss an example of a hypothesis testing with unknown population variance and the use of the Central Limit Theorem. Cheers! ;-)

In this lecture, the concepts involving hypothesis testing for paired samples with small sample sizes are discussed. It is recommended that you use a graphing calculator for the calculations of the t-statistics. Please feel free to download the notes for your reading. There is no lecture video. Cheers! ;-)

In this lecture, I will discuss the basic concepts involving hypothesis testing type I and type II errors. Cheers! ;-)

In this lecture, there are two practice problems on Hypothesis Testing. One problem is to conduct the test with known population variance, and the other problem is to conduct the test with unknown population variance. For hypothesis testing with unknown variance, remember to calculate the unbiased estimate before you proceed to determine the p-value or the calculated z-score.

Please download and attempt the questions before you check the answers. Cheers! ;-)

A Chi-Square Test for Independence is usually applied when you have two categorical variables from a single population and the test is applied to determine if there is a significant relationship between the two variables. To calculate the Chi-Square probability, it is recommended that a graphic calculator is used. Please refer to the attached notes for an introduction to the Chi-Square Test of Independence. ;-)

In this lecture, I will do a brief introduction to the concepts involving Correlation and Regression. Cheers!

In this lecture, I will introduce the basic concepts of linear regression lines, including the Least-Square method to obtain the lines. Cheers! ;-)

In this lecture, I will discuss about the concepts involving the product moment correlation coefficient and covariance. Do take note that the concept of covariance is not included in the GCE A level syllabus for H1/H2 Maths. Cheers! ;-)

In this lecture, I will present the materials to explain about the linearization of non-linear bi-variate data. Linearization is necessary when we need to develop the linear regression line as the most suitable model for the bi-variate data.

Please download the notes for your reading. There is no teaching video at the moment. Cheers! ;-)

One important question to ask about correlation is: “How large must the correlation coefficient be before we can conclude that a significant correlation exists between the two variables?”. In this lecture, we will apply hypothesis testing to check the significance of a correlation between two variables. Please download the notes for your reading, There is no teaching video at the moment. Cheers! ;-)

In this lecture, I will present an example of a correlation and regression question. Please look through the example and its solutions carefully. There is a practice problem in this lecture. Please download and attempt the question before checking the solutions.

There is no teaching video at the moment. Cheers! ;-)

These are the solutions for Quiz 1 and 2. Cheers! ;-)