Random Variables

We talked before about probability using simple sample spaces, but in reality, we will map situations to probabilistic models that cater to all possible results. The variables to which we are going to construct probabilistic models are called random variables.

Conditional Probability

For any two events A and B, with \(\mathbb{P}(B) > 0\), we define the conditional probability of A given B (\(\mathbb{P}(A|B)\)) as \[\mathbb{P}(A|B) = \frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}\] Example: We throw a dice once, and it lands on an even number.

Introduction to Probability

Probability is at the heart of statistics, as most of the time, we won’t have the entire dataset to work on. Still, instead, we will need to understand how the population works relying on a sample.