Definition with example:
The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable, i.e. what is the possible number of times that head might occur? It is 0 (head never occurs), 1 (head occurs once out of 2 tosses), and 2 (head occurs both the times the coin is tossed). Hence the random variable is “getting head” and its values are 0, 1, 2. now probability distribution is the probabilities of all these values. The probability of getting 0 heads is 0.25, the probability of getting 1 head is 0.5, and probability of getting 2 heads is 0.25.
There is a very important point over here. In the above example, the random variable had 3 values namely 0, 1, and 2. These are discrete values. It might happen in 1 certain example that 1 random variable assumes 1 continuous range of values between x to y. In that case also we can find the probability distribution of the random variable. Soon we shall see that there are three types of probability distributions. Two of them deal with discrete values of the random variable and one of them deals with continuous values of the random variable.
Difference between probability and probability distribution: In probability we do not repeat the same event more than once. If the same event is repeated more than once, we calculate probability distribution. For example, to find the probability of getting head in tossing a coin once is an example of simple probability but when the coin is tossed more than once, we get probability distribution.
Here, the number of times the event occurs or is repeated is known as the number of trials and is represented by N.
Types of probability distribution:
1. Binomial distribution: Deals with discrete...