What is the PDF of Z the standard normal random variable?
A continuous random variable Z is said to be a standard normal (standard Gaussian) random variable, shown as Z∼N(0,1), if its PDF is given by fZ(z)=1√2πexp{−z22},for all z∈R.
What is the distribution of the random variable Z where Z x − µ )/ σ?
standard normal distribution
The standard normal distribution has a mean of zero and a variance of one. If the behaviour of a continuous random variable X is described by the distribution N(µ, σ2) then the behaviour of the random variable Z = X − µ σ is described by the standard normal distribution N(0,1).
What is the z-score of X 9 if it is 1.5 standard deviations to the left of the mean?
-1.5
Since 9 is 1.5 standard deviations to the left of the mean, z = -1.5.
How is the notation x Sim n ( \\ Mu, \\ Sigma ^ 2 ) read?
Dilip’s answer also gives a nice account of what other possible interpretations there are when the notation is less clear than σ2, e.g. for general parameters {a, b}, viz. X ∼ N(a, b). Whenever I see this notation in text I tend to read it so that it makes sense grammatically. I would claim that this the sensible way to treat the notation.
What does N ( μ, σ2 ) mean in statistics?
The difficulty is not in knowing what N(μ, σ2) means. Even N(3, 52) is reasonably unambiguous to most peaople as meaning a normal random variable with mean 3 and variance 52 or variance 25 (purists should believe that the standard deviation is a more fundamental parameter than the variance should free to say “standard deviation 5 ” instead).
How to say that X follows a normal distribution?
Putting it all together, you have a random variable X which is distributed as Normal with a mean “mu” ( μ) and variance “sigma squared” ( σ2 ). You can also say X follows a normal. . .
How to write the notation n ( μ, σ2 )?
If they are not independent, you can say that Xi, i = 1, 2, …, n are possibly dependent, but (marginally) identically distributed as N(μ, σ2). Or you may have to instead declare their joint distribution — that depends on what purpose you have for considering the random variables.