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Standard Normal Distribution with examples using Python

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Difference between Discrete and Continuous Random variables

Difference between Discrete and Continuous Random variables

What is a Random Variable?

Let's say you want to observe the number of goals scored in any football match in the English Premier League season. You record the number of goals scored in each match in a set S--> (3,1,4,0,6,8,...2). We just conducted a series of random experiments of observing goals in each match. Every random experiment had a numerical outcome which we call as a random variable. In our case, it was the number of goals in each match (3,1,4,...2). The reason we call this as random is because we do not know until the end of the match about the number of goals which would be scored.

What is a Discrete Random Variable?

In our example of observing number of goals scored , we saw the set S--> (3,1,4,0,6,8,...2). A match can end in a draw (0 goals), or the number of goals could be 1 or 2 or n goals. The n goals will be finite and sensible. In some sense, we can count the number of goals or we can say number of goals is a whole number from 0 to n. n cannot take values like 1000, 500 for this experiment. Hence we call this as a discrete random variable as it is countable. Other examples of a discrete random variable could be number of students passing an examination, number of chairs in a classroom.

What is a Continuous Random Variable?

There are other forms of random experiments as well. Let's say I want to observe non-stop flight duration from Bangalore to Delhi each day for 1 month. Assuming only 1 flight each day the set S (in minutes)--> (160 , 150 , 200,201, 205, 207...234) . We have infinite number of choices for the flight duration. If we track at a second level, we may have values like 160.75, 160.25, 201.34 and so on. So the continuous random variable can possibly take infinite values. A discrete random variable can take finite values. Other possible continuous variables could be avearge temperature in a city on a given day , average duration of phone calls done by people between 7pm to 9pm.

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