>mathematician arbitrarily chose the expected value, E[X]

>>8420658
>derivative of |x| is a fun thing to work with

File: what.jpg (26KB, 450x274px) Image search: [Google]

26KB, 450x274px

>>8420660

it is true tho, how the fuck do you interpret the currently accepted E[X] in words? The squaring removes any meaning from it

That's a very strange definition you have there. Pretty sure you mixed something up.
Reference?

File: you get the idea.png (11KB, 1588x123px)

11KB, 1588x123px

>>8420667

this is for when the domain is N, but you get the idea.

File: i mean the variance.png (3KB, 607x111px) Image search: [Google]

3KB, 607x111px

>>8420667
>>8420676

wait, I meant the variance, not the mean, the mean makes complete sense.

>>8420658
Also, on re-read, you fucked up OP:
[eqn]Var(X) := E[(x_i - \bar{X})^2] = \sum_i p_i (x_i - \bar{X})^2 [/eqn]

>>8420691

yea well whatever, i meant the variance.

>>8420695
>Perhaps you can say what is confusing you
Var(X) is just the 'sum' of of squared distances from the mean, weighted by the probability of observing a given [math]x_i[/math].
> sum here being a placeholder for either summation or integration

>>8420709

why the arbitrary choice of squaring it, why not use the absolute value of it. Like I said >>8420666

>>8420715
If X and Y are independent, then Var(X+Y)=Var(X)+Var(Y). This would not be true if you used the absolute value instead of the square.

>>8420715
What would the central limit theorem look like if our standard were based on the absolute value? From a practical perspective, we get a lot of mileage out of the CLT.

>>8420728 makes an equally good point, and is again grounded in the notion that 'it is easier to work with'.

Also, what you are proposing/asking about, [math]E[|x_i - \bar{X}|][/math], is sometimes used, depending on the context.

>>8420751
>What would the central limit theorem look like if our standard were based on the absolute value?

There is just a constant factor between the standard derivation and the average distance to the mean for a normal distributed variable. A normal distributed random variable [math]X [/math] has the property that

[eqn] V(X) = E[(X - E(X))^2] = \frac{2}{\pi} \left( E[|X - E(X)|] \right)^2 [/eqn]

>>8420788
But we don't parameterize the normal distribution this way.

File: Capture6.png (11KB, 741x154px) Image search: [Google]

11KB, 741x154px

>be pissed off at this thread
>forgot that I recently started browsing /g/ and installed Noscript