The Normal Density
There is a plethora of books on probability and statistics that cover the important normal distribution, and I recommend one among many excellent texts, the volume by Ross , especially Chapters 5, 6, and 7, where most of the elementary facts can be found.
Recall that a continuous random variable X is normally distributed with parameters μ and σ if its density function is defined, for all i, by
It is known that E(X) = μ and Var(X) = σ2. Suppose we have n independent samples X1, X2, . . . , Xn from a normal distribution having an unknown mean that is now designated as θ in order to be consistent with the notation ...