This was a question on my exam and I am not sure I did it correctly. Can someone show me the steps to derive it?
Given X1, X2, X3, X4 are random uncorrelated variables with variance of 1 and mean of 0. Find the correlation coefficient for (X1 + X2 and X2 + X3).
I got the answer as -1/2. is this correct?
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.
Using Central Limit Theorem:is the square root of the variance calculated above.
Therefore P(-2 <= x <= 2) = 0.512
At a bank, the interest is calculated on 100 accounts and rounded up or down
to nearest cent. If it is assumed that the round-off error is uniformly distributed between
(-1/2, 1/2) and
the round-off errors are independent, find the probability that the sum
of the error does not exceed 2 cents in magnitude.
I dont understand how to calculate the variance for just one account. the answer for variance for just one account is 1/12.
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 + · · ·
"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?
The degree of the polynomial is the highest degree in the polynomial.
has 3 as the highest degree, so the degree of the polynomial is 3.
Adding and subtracting polynomials is just like adding and subtracting numbers. You collect the like terms(the terms which have the same degree) and add or subtract them together.
First you take care of the negative sign:
Then group the like terms together:
And now add or subtract:
Follow these rules and try the questions you have posted again. Post your answers here, so we can see where you went wrong.
PS Also look at the links bobbym posted
A circular hot plate given by the relationship x^2 + y^2 <= 4 is heated according to the spatial temperature function T(x, y) = 10-x^2 + 2x - 4y^2. Find the hottest and coldest temperatures on the plate and the points at which they occur.
Here is what I have so far:
g(x,y) = x^2 + y^2 - K where K<= 4
del f = (-2x + 2, -8y)
del g = (2x, 2y)
Applying LaGrange multiplier
1) -2x+2 = lambda(2x)
2) -8y = lambda(2y)
3) x^2 + y^2 = K
solving for eqn 2)
we get y=0 or lamba = -4
sub lambda = -4 in eqn 1
we get x = -1/3
now I am stuck, since there are infinite values of K we have to solve for. I know there is going to be points (-1/3, +/- y) and (+/-x, 0).
Another approach that gives me half the answer is solving for the global max of T(x,y), which coincidentally lies in the constraint given, but then I am at a loss at finding the local min.