How can I show that the average( x - average(x^2) ) = average(x^2) - (average(x))^2 ?
Thanks for any help
Frankly, what you have written is non-sense. It makes no sense to talk about the average of a single value. I suspect you mean that x is a random variable and that the "average" is the expected value or mean. Now, if so, what is the definition of "expected value" of a random variable?
Ok, let me try to clear things up. It shows up in this problem as
standard deviation = sqrt( average( c - average(c) )^2 ) where c = speed in this case. I am given a hint that I should show that average( c - average(c) )^2 = average(c^2) - average(c)^2
You can take average(c) as constant here and the other c is a variable. I guess that notation is confusing but hopefully that clears things up.