Statistics Notation: Mean, Variance & Normal Distribution

[ampakine]

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?

 

[Stephen Tashi]

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


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?

In probability theory, the notation is used to state the distribution for a random variable. You may think of the "~" as saying "distributed as" or "with distribution" or "has distribution".

Also the N(μ, σ²) I assume means normal distribution but is that some kind of standard notation for distributions?

It's a standard notation for normal 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?

Yes

 

[ampakine]

That clears it up. Thanks!

 

[QuendeltonPG]

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

Just to say it would be a normal with a mean of 23 and a variance of 9.

 

[Stephen Tashi]

Just to say it would be a normal with a mean of 23 and a variance of 9.

Yes. My mistake. The notation did use a $$\sigma^2$$ so the 9 is the variance, not the standard deviation.