Question 1)
I have X and Y independent stoch. variables
What is E[X^2 * Y | X] ?
does it generally hold that if X and Y are independent, then every function of X (eg X^2) is independent of Y?
Does E[X^2 * Y | X] then become E[X^2|X]*E[Y|X] = E[X^2|X]*E[Y] since X^2 is independent of...
Hi,
I'm in a college statistics course where I'm doing an assignement with Minitab.
I have a one month time series of electricity use (hour intervals).
I've attempted to remove the season effect from weekdays by index multiplication so all I'm left with (hopefully) is the effect from...
tiny-tim, Thank you, I found a guide on Wikipedia that proved very helpful.
HallsofIvy: Then I obviously didn't know long division, I didn't know you could use that to figure out the decimal value of the remainder. Your explanation helped.
Thanks
I'm working on moving away from long time slavery to the calculator
Most forms of division and multiplication is going well now (long division and in some instances lattice multiplication)
One thing I DON'T get though (and can't find any guides for) is dividing remainders.
For example...
I have (from a complex equation problem) found the following angles in the answers:
5PI/8, 9PI/8, 13PI/8, 17PI/8
In the same assignement I found sin(PI/8) = .5*sqrt(2-sqrt(2)) and I found the cos(PI/8) value by using standard trig. identities.
Is there an easy way to use this result to...
Ok, so I have two questions regarding something I don't understand in my textbook (Adams)
1.
0 if 0<=x<1 or 1<x<=2
f(x) = 1 if x=1
(by "<=" i mean less than or equal)
I'm supposed to show that it is Riemann integrable on that interval.
They chose P to be: {0, 1-e/3...
Oh, but I didn't think I could do that when y*x^2 was encapsulated by parantheses.
When I solve what you posted I get y=tan^-1(x) but the answer is supposed to be:
(pi/4)(1/x^2)-(1/x)-tan^-1(x)/x^2
(the pi/4 comes from the start value...)
Oh, dear god... I can't believe I could be THAT silly :bugeye:
Of course I see it, my incredible dull brain was confused by the n's, probably.
Anyways, sorry for bothering you with this. That was rather embarrassing...
So I am supposed to find the distance from the moon where the force on a particle from the Earth and sun is equal.
I get this expression (earth-moon distance is 400 000km):
yMm/(r^2) = yMm / (400000km-r)^2
But from that I get r=200 000km and the answer should be 40 000km...
whats wrong...
Ok, thanks. I have that one now.
Can you please hint me with one more:
I have the integral of (sqrt(1-x^2)) / x^4 dx
Which with trig.subs leads to:
integral of cot^2(y) *csc^2(y) dy
Again I'm stuck :P
Ok so after a substituion I have this: (I don't know how to proceed)
"integral of" (u-2) / sqrt(u^2 + 1) du
and by the way, can someone tell me what cot^3(tan^-1(x)) equals?
Thanks!
Yeah, thanks. I made it to the last step, but I don't see what happens with the Cos bit... :P
(EDIT: The cos bit in the solution of the integral of Tan phi)
Ok, so I have the integral of (x^2 + 1) / (x^3 + 8) dx
I use partial fractions and end up with two integrals, the one I cannot solve is:
1/12 * "integral of" (7x-4) / [(x-1)^2 +3 ] dx
With u=x-1 I get
(7u-3) / (u^2+3) du
But I have no Idea of how to solve it, the answer in the books...
Hi
So I am a little confused about the absolute value sign here. Is the derivative right:
[x-1/|x-1|]e^x + |x-1|e^x
But what do I do when I set this to zero? Do I get two expressions, one for x>1 and one for x<1 ? (thus removing the absolute value signs)
Hi
I have found the following TP (n=4) for g(x) = (1+5x)^1/5
P4(x) = 1+x-2x^2+6x^3-21x^4
Then they ask me to show that 0<E4(x)<80x^5 when x>0.
I don't know how to start, or exactly what I am supposed to show...?
I have found E4(x) to be( 399/[5(1+5X)^24/5] ) *x^5...
And 0<X<x ...?
Ok so I have found a formula for d^n/dx^n 1/x^2
= (-1)^n * (1+n)! * x^-(n+2)
So I have to do d/dx [(-1)^n * (1+n)! * x^-(n+2)] and see what I end up with. But how do I do that.
My book gives an example: (from d/dx (1+x)^-1)
d/dx [(-1)^k * k!(1+x)^(-k-1)] = (-1)^k *...