We will cover a few key concepts before moving on to the body of the chapter:
- In the case of discrete distribution, a probability mass function is used to find out the probability, p(X= x), where X is a discrete random variable and x is a real value number.
- In the case of continuous distribution, probability density function is used to find out the probability p(X <= x). In this scenario, a probability curve is plotted and the area under the curve (integration) helps us with the probability.
- Conditional probability is to understand this, a cricket match can be the perfect example. Suppose there is a game scheduled between India and Australia and we are trying to pass on our belief of India triumphing. Do you think that the probability will be impacted by the team selected by India? Will the probability of India winning the match be impacted if Virat Kohli and Rohit Sharma are part of the team? So, p(India winning|Rohit and Virat are playing) denotes the probability of India winning, given that Rohit and Virat are playing. Essentially, it means that the probability of one event is dependent on the probability of another event. It is called conditional probability.
The probability of x, given y, can be expressed as follows:
- The chain rule computes the joint distribution of a set of random variables using their conditional probabilities. From conditional probability, we know that
.
It implies that if there are 
events. The joint probability distribution turns out like this:
