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