# Continuous random variable and the normal distribution

How are we going to know that a continuous random variable is a normal random variable? The definition I believe for a continuous r.v. to be a normal r.v. is that it's probability density function must be the pdf of the normal distribution. How are we going to check the pdf of a continuous r.v. and compare it with the normal distribution?

I really need the help. Thanks guys.

• What is your rv? – TheSimpliFire Oct 23 '17 at 9:58
• Just some random continuous rv. I'm trying to find whether there exist a procedure that one must do in order to check whether a continuous rv is a normal rv or not. – Isaac Newton Oct 23 '17 at 10:00
• It sounds like: how to find out that a piece of fruit is an apple? – drhab Oct 23 '17 at 10:00
• Do you have an equation? Dataset? Without more information, not much to be done. Maybe graph a histogram of your data and fit it with the normal pdf. Try a statistical test, like KS-test, which compares the cdf. – jdods Oct 23 '17 at 10:00
• Compare the pdf of your rv with $\frac{1}{\sigma \sqrt{2 \pi}} \textrm{exp}\left[-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2\right]$ – TheSimpliFire Oct 23 '17 at 10:03

If you have certain data regarding your specific random variable, one of the methods to deduce its distribution is the so called statistical inference, where you try to find the distribution (and respective pdf) that best fits your data. Sometimes you're only interested in some properties of the random variable, like its mean or variance, and not necessarily the distribution itself.

There are parametric and nonparametric approaches to this, you should check these definitions carefully.

• Can you site a reference where I can do some readings this Statistical Inference? I'm really interested in nailing if it is a normal rv or not. – Isaac Newton Oct 23 '17 at 10:10
• The book 'All of Statistics' by Larry A. Wasserman is pretty good. – sam wolfe Oct 23 '17 at 10:40
• Does this book specifically tackle the issue that Im facing here. Do you happen to have an electronic copy of it? :) – Isaac Newton Oct 23 '17 at 10:49
• It might provide you with an insight on what's behind statistical inference. If your issue is simply comparing the pdfs, then you do it directly by looking at both of them. No I don't. – sam wolfe Oct 23 '17 at 11:00
• Ah. Thanks for your help :) – Isaac Newton Oct 23 '17 at 11:01