Chapter 3: Normal Distribution

Normal Distribution is the father of all probability distributions. For larger sample size almost all theoretical distributions follow it.

Details

In this course, we inspect the probability distribution for a continuous random variable.
We know that, if a random variable X can assume any value of real set R or within any interval of real set R, then it is called a continuous random variable. If a random variable can assume any value between the definite interval a to b, then it is denoted by a < x < b.

A function for obtaining probability that a continuous random variable assumes value between specified interval is called the probability density function of that variable and it satisfies the following two conditions:

1. The probability that the value of random variable lies within the specified interval is non-negative.
2. The total probability that the random variable assumes any value within the specified interval is one.

Normal distribution is a very important probability distribution among probability distributions for continuous random variable and is very useful for higher statistical study.


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