I've got a tricky computational statistics problem and I was wondering if anyone could help me solve it.
Okay, so in your left pocket is a penny and in your right pocket is a dime. On a fair toss, the probability of showing a head is p for the penny and d for the dime. You randomly chooses a...
Hey guys, I'm trying to find a conditional distribution based on the following information:
##Y|u Poisson(u \lambda)##, where ##u~Gamma( \phi)## and ##Y~NegBinomial(\frac{\lambda \phi}{1+ \lambda \phi}, \phi^{-1})##
I want to find the conditional distribution ##u|Y##
Here's what I've got so...
Hey guys, I was wondering if you could help me out with a question I've got, I really don't know where to go or really where to start! Here's the question:
Let S be a subspace of a finite dimensional vector space V. Show that there exists a Linear Mapping L: V → V such that the kernel of L is...
Ok, but there's this example in my textbook:
\sum^{n=1}_{infinity}(1/2)^{n}=\frac{1/2}{1-(1/2)}=1
"The series is a geometric series with a=1/2 and r=1/2"
I'm confused as to how a=1/2
Oh! Everything would cancel out except a - ar^n
S - r*S = a - ar^n
...
S = a(1 - r^n)/(1-r)
which explains why -1<r<1 since the limit n->inf r^n would diverge above 1
But judging by what everyones been saying, I'm assuming if n=1, then the sum is a/(1-r) and if it starts at 0 you have to multiply everything by r, making the actual sum ar/(1-r)
EDIT: n=1 to infinity of course
I'm confused about the sum of the geometric series:
\sum ar^{n-1} = \frac{a}{1-r} when |r|<1
but if you have a series like:
\sum (1/4)^{n-1}
the sum is:
\frac{1/4}{1-(1/4)}
should't it be \frac{1}{1-(1/4)} because there is no a value?
I ended up using trial and error and I ended up with N=4. I'm not sure if there's a better way to find M, but I made a list of derivatives and found it that way and that worked! Thanks!
I must have copied down the formula wrong, woops!
Im still not understanding.. I can find the error when finding an approximation for the series, but I don't understand how to find an approximation of the series when I have an error...
[PLAIN]http://img600.imageshack.us/img600/1210/11096142.png [Broken]
Hey I was wondering if you guys could help me out with this question...
I think I have the right power series:
= \frac{1}{1-x} + \frac{x}{1-x}
= (1+x+x^{2}+x^{3}+...)(x+x^{2}+x^{3}+x^{4}+...)
=...
Ok, I understand that, but what's the difference between conditional convergence and absolute convergence? I always thought it was just 1s and 0s, it either converges or not, but conditional convergence is in between? Does is converge slower or something?
So I have this series:
\sum^{infinity}_{n=3}(-1)^{n-1}\frac{ln(n)}{n}
And I'm trying to use the AST to find out if it converges or not.
First of all, I'm stuck trying to show that ln(n)/n is decreasing...
But then after that. I'm assuming I can compare it with 1/n to show that it...
I'm sure it doesn't, but how do I find out?
\sum^{infinity}_{n=1} arctan (n)
I thought about using the integral test, but it's not decreasing. Any hints?
Could I somehow use proof by induction to show that its an increasing function?
Ohhh! I get it, thanks! About part c)... distance = velocity x time, so would I just multiply my equation by t? I can't seem to wrap my head around this stuff
[PLAIN]http://img204.imageshack.us/img204/11/60272414.png [Broken]
Hey guys, I'm stuck on this question, part b)
I figured out a) and v(t) for V(0) = 0 ends up being
mg - mge-kt/m
k
(Sorry, latex was being difficult)
But then when I try to figure out the limit...
I'm having trouble with part a) of this question...
[PLAIN]http://img69.imageshack.us/img69/5815/98157006.png [Broken]
So I started off by solving the DE above a), and I've gotten it down to:
\frac{1}{2} m v^{2} = \frac{mgR^{2}}{(x + R)} + C
I can tell I'm getting close, but I'm a...
So I've gotten the integral that I'm doing now down to:
int(cos(x)/sin^2(x) dx)
I looked it up on one of those online integral calculators to get me on the right track, and the answer is:
-1/sin(x)
It seems so simple, what am I missing?
\int x^{2} \sqrt{4+x^{2}} dx
I've already subbed in:
x = 2tan\theta
dx = 2sec^{2}\theta d\theta
and I've gotten down to:
16 \int tan^{3}\theta sec^{3}\theta d\theta
But now I have noo idea what to do! Can someone give me a hint?
I'm still not seeing what you're saying... You can differentiate F(4)-F(2x), it would be F'(4)-F'(2x), meaning the answer is what I said first? 4*cos(4) - 2x*cos(2x) ?
Ahh all this theory stuff makes my head spin :cry:
Oh, I guess I was reading FTC part II wrong =P so I would have to integrate t*cos(t), making the answer...
dy/dx[4*sin(4) + cos(4)] - [2x*sin(2x) + cos(2x)] ?
(Not quite sure how to use Latex so I print screened it :tongue:)
[PLAIN]http://img87.imageshack.us/img87/5991/calc1.png [Broken]
So I've been staring at this question, and I think I might have it but I'm not 100% sure, is the answer just
t*cos t |42x = (4)*cos(4) - (2x)*cos(2x)
?
Or...