## Joint distribution :

Joint distribution refers to the probability distribution of two or more random variables. This means that the joint distribution describes the likelihood of each possible combination of values for the random variables.

One example of a joint distribution is the probability distribution of the number of heads and tails in a series of coin flips. In this example, the two random variables are the number of heads and the number of tails. The joint distribution would describe the probability of each possible combination of the number of heads and tails, such as a distribution where there is a 50% probability of getting two heads and zero tails, or a 25% probability of getting one head and one tail.

Another example of a joint distribution is the probability distribution of the heights and weights of a group of people. In this example, the two random variables are the height and weight of each person in the group. The joint distribution would describe the probability of each possible combination of height and weight, such as a distribution where there is a high probability of finding people who are both short and light, or a low probability of finding people who are both tall and heavy.

In both of these examples, the joint distribution provides important information about the relationship between the two random variables. For example, in the coin flip example, the joint distribution may show that the probability of getting a certain number of heads is directly related to the probability of getting a certain number of tails. In the height and weight example, the joint distribution may show that there is a strong relationship between height and weight, such that people who are taller are more likely to be heavier.

Overall, the joint distribution is a useful tool for understanding the relationship between multiple random variables and the likelihood of different combinations of their values. By using joint distributions, researchers and analysts can gain insights into the underlying patterns and trends in complex data sets.