Please help on arithmetic mean of continuous distributions.

[AAQIB IQBAL]

PROVE mean (X bar) of a continuous distribution is given by:

∫x.f(x)dx
{'a' is the lower limit of integration and 'b' is the upper limit}

 

[chiro]

PROVE mean (X bar) of a continuous distribution is given by:

∫x.f(x)dx
{'a' is the lower limit of integration and 'b' is the upper limit}

Hello AAQIB and welcome to the forums.

I think the best way would be to first prove the case for the discrete case and then use integral definitions in calculus to prove the integral way.

If you haven't taken a thorough course in calculus, you'll find that the integral is simply a special kind of limiting sum, just like the differential is a quantity that is calculated through a limiting argument.

Note as well that we can't just give you the answer, we ask that you show your working so we can provide hints and let you attempt to figure it out so that you learn for yourself.

So in this spirit, can you first prove the discrete version of the expectation theorem?