Chapter 3: Normal Distribution

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

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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.