In my lecture notes on confidence intervals the lecturer wrote this:

Recall that measurements tend to follow a normal distribution. To describe the normal distribution and answer useful questions (as in the previous chapter), we need to know two numbers; the expectation or mean μ and the standard deviation (square root of the variance) σ. Then the quantity we measure X follows the normal distribution:

X ~ N(μ, σ²)

 

I don't understand the notation of that bolded text. I know X is a random variable, μ is the population mean and σ is the population standard deviation but what does the ~ mean? Also the N(μ, σ²) I assume means normal distribution but is that some kind of standard notation for distributions? For example if I said N(23,9) would that mean the normal distribution with a mean of 23 and standard deviation of 9?

Edited April 29, 201114 yr by ampakine

In statistics and probability theory, ‹~› means “is distributed as”.

For example if I said N(23,9) would that mean the normal distribution with a mean of 23 and standard deviation of 9?

 

note that if indeed it says [math]\sim N (\mu , \sigma^2)[/math] then the 9 is the variance not the standard deviation, the latter being the square root of the former, of course.

Edited April 30, 201114 yr by Bignose

It has been a while but I think- N is the population size, mu is the population mean, and sigma squared is the population variance. SM

 

NOTE- edited to comply with the recollections of M.

Edited April 30, 201114 yr by SMF

It has been a while but I think- N is the population size, mu is the population mean, and sigma squared is the population variance. SM

 

NOTE- edited to comply with the recollections of M.

 

No, Xitten has it right. "~" should be read as " is distributed as" and N means normal. [math]X \sim N(\mu , \sigma^2)[/math] in words means X is distributed normally with mean [math]\mu[/math] and variance [math]\sigma^2[/math].