Properties of the Distribution

Calculation of Mean and Variance

To calculate the mean of the Uniform distribution, we can simply integrate over x *(Uniform PDF), per the definition of mathematical expectation.

> restart;

> with(plots, display):

> f(x):=UniformPDF(alpha..beta,x);

[Maple Math]

> EX:=simplify(int(x*f(x),x=alpha..beta));

[Maple Math]

Notice that E( X ) is midway between alpha and beta.

Calculating Var( X ), we will employ the formula: Var( X ) = E( [Maple Math] ) - [Maple Math]

> E_X_SQ:=int((x^2)*f(x),x=alpha..beta);

[Maple Math]

> VarX:=simplify(E_X_SQ-EX^2);

[Maple Math]

Notice that Var( X ) simplifies to [Maple Math] .