Probability & Statistics

Success Criteria

At the end of this chapter, students are able to:

1. Find the total number of permutations of a subset of objects.

2. Find the total number of combinations of a subset of objects.

3. Calculate conditional probabilities, P(A | B).

4. Calculate the probability of an event modelled by the binomial distribution, B(n, p).

5. Calculate the mean and variance of a binomial distribution.

6. Calculate the probability of an event modelled by the normal distribution, N(μ, σ²).

7. Perform a univariate linear regression.

8. Interpolate and extrapolate a linear regression.

9. Apply a linear law transformation to perform a univariate non-linear regression.

Introduction to Combinatorics, Probability & Statistics

Before we dive into the wonderful world of statistics, we need to first begin with Combinatorics, which is a subfield of discrete mathematics that deals with the Art of Counting (How many ways can I arrange this?). We need a methodical approach to counting different combinations and arrangements of objects & events so that we neither over-count nor under-count.

Probability is the Study of Chance (How likely is something going to happen?) is then built on combinatorics. Before we can assign probabilities to events, we must first know the total number of possible outcomes and the number of favorable ones. 

Once established, probability becomes the backbone of Inferential Statistics. Statistics at its core is the Sensemaking of Data (What does the data tell me?). It can be divided into 2 major branches (Descriptive and Inferential). 

• Descriptive Statistics (Eg. Pie Charts, Percentiles, Standard Deviation) is about summarizing and describing data we have collected. 

• Inferential Statistics takes the incomplete set of data (Sample) we have collected a step further by applying probability theory to make predictions or draw conclusions about a larger group (Population).