S2 - Continuous uniform distribution

In the textbook it says that you should be able to derive

E(X)=\frac{a+b}{2}

Var(X)=\frac{b-a}{12}

, from first principles.

Could some one please tell me how to derive

Var(X)=\frac{b-a}{12}

using integration? Will a question asking for the proof come up in the exam?

(edited 11 years ago)

\displaystyle \int x^2 f(x) dx -\mu^2

It's in all the formula books.

Var(x)=\displaystyle\int^b_a \frac{x^2}{b-a}\ dx - (\frac{b+a}{2})^2

You can expand this and see see where you get :wink:

\displaystyle \int x^2 f(x) dx -\mu^2

It's in all the formula books.

Original post by dan94adibi

Var(x)=\displaystyle\int^b_a \frac{x^2}{b-a}\ dx - (\frac{b+a}{2})^2

You can expand this and see see where you get :wink:

Thank you both :smile:

I'll take your advice and expand it and see how it goes :biggrin:

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