Let’s start by defining the two types of numerical variables: discrete and continuous.

**Discrete variables —**This represents the countable number of values. For example, we can count the number of boxes in a carton. A carton can contain 20 boxes and if you take one out, then it contains 19 boxes.**Continuous variables—**This represents measurements. For example, the weight of the carton can assume possible weights of 40 grams, 40.01 grams or 40.00001 grams depending on how granular you want to get.

Let’s take a real-world example, the most common one — A fair coin:

**Event**— A possible outcome of doing something. In tossing a coin, we can either get a head or a tail**Experiment**— An act that produces an event. Here it is the action of tossing the coin**Sample Space**— It is the set of all possible outcomes of the experiment. Here there are 2 possible outcomes. Hence the sample space is 2**Probability**— The chance of an event occurring. If we toss a coin, the chance of head occurring is 1/2 = 0.5 = 50%**Mutually Exclusive Event**— 2 events are mutually exclusive if only one can take place at a time. In our example, only a head or a tail can occur at each experiment**Independent Events**— The outcome of one event is not impacting the next event. If we toss the same coin 2 times, the fist outcome being a head or a tail does not affect the second outcome (If you draw cards, the second draw will have only 51 cards. Hence they are not Independent events)

A distribution is a formula that can calculate the probability of occurrence of a data point in a set of data points. Now, we can look at the types of distributions

There are hundreds of probability distributions however, an experienced statistician probably has probably only worked with about 12 of them. So for today, we will focus only on 3 of the most commonly used distributions.

- Binomial Distribution
- Normal Distribution
- Poisson Distribution

Note: They may take any shape but the combined probability of all outcomes of a distribution is always 1.

While Normal Distribution deals with continuous values, the Binomial and Poisson Distribution deals with **discrete **values.

Quick Question: Is the outcome of tossing a coin continuous or discreet?

This is the simplest distribution that is used to describe** discrete data**. As the name suggests, there can be only 2 outcomes to an experiment in binomial distribution. From our earlier examples, a coin toss can result in either a head or a tail. Similarly pass or fail, yes or no outcomes follow this distribution.

Let’s start with a random variable X that equals to the **outcome of the event getting all heads from flipping a fair coin 3 times**. The number of heads flipped in the 3 trials can be as low as 0 or all 3 turns can out to be heads.

Looking at the likely outcomes (because it is easy to count): TTH, THH, HHT, HTT, THT, HTH, HHH, TTT. The sample space is 8

Now, what we want is the probability of flipping heads in 3 trials. You can see from the above list that out of the 8 possible outcomes, it occurs only once:

P(X=3) = 1/8

What are the other possible outcomes here? No heads, 1 head, 2 heads and all 3 heads.

- P(X=0) = 1/8
- P(X=1) = 3/8
- P(X=2) = 3/8

If you try plotting it, you can get a graph like the below.