Math Is Fun Forum

anon: Yes both flavors xi and yi are the same.

Elaina: No those two are not the same, they differ since both the yi's and si's are different. No both flavours can be same as long as the size is different.

Hi Bob Bundy,

I am asking for the Correlation coefficient of X1 + X2 and X2+X3. Not X1+X2 and X3+X4.

I agree with your answer if it was that .

Hi bobbym,

Yes that is the correct answer. I was asking about calculating the variance not the probability.

Var(X) = E(x^2) - E(x)^2

and f(x) = 1 as this is uniform distribution from -1/2 to 1/2.

so:

Using Central Limit Theorem:

Therefore P(-2 <= x <= 2) = 0.512

It should be the largest number which is the sum of the maximum number of distinct primes.

Hey

The negative sign does not "belong" to x, think of it as -1 * x = -1x = - x.

Does that make sense?

hi,

Almost correct! It is

Btw i just solved it by chance.

Good luck...also i believe after prime 550, the sum come to more than a million, if you start from the 4th prime.

Heres an infinite series "proof" that shows 0 = 1

0 = 0 + 0 + 0 + 0 + · · ·
= (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) + · · ·
= 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + · · ·
= 1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + · · ·
= 1 + 0 + 0 + 0 + · · ·
= 1

"Legend has it that, around 1703, in letters to contemporary mathematicians, an Italian monk by the name of Guido Grandi (often called Guido Ubaldus) presented this as proof of the existence of God, since it suggested that the universe could have been created out of nothing! What he actually meant isn't clear, but we do know that the brightest minds of the day were unsure how to explain what the problem was. Leibniz at least recognized that the problem was in the ____ line above;"

I left it blank intentionally

This is copied from my Calculus prof notes, he showed is this "proof" in class.

Hi Bob bundy,

Can you verify my calculations below(just for my understanding):

now from here convert to polar co-ordinates
EDIT: I am not sure what the integration limits for theta would be...if it is 0 to pi/2, then this works out.

let u = r^2, du = 2rdr

since we squared the original equation, we square root the final answer so

This doesnt agree with what wolfram and wikipedia get . Any idea where I went wrong?

Thanks

Hahaha I could not have thought of that on the final exam. Lost 10% right there .

Thanks Bob