Hey There,
I was just wondering if there were any people available on the site who could give me advice for which course to take in the upcoming fall 2010 semester. I'm an undergraduate chemistry and math major, nearing the end of my studies (1 year remaining). I have a math elective to...
Homework Statement
LEt X have a Poisson distribution with u=100. Use Chebyshev's inequality to determine a lower bound for P(75<x<125)
Homework Equations
Chebyshev's Inequality.
The Attempt at a Solution
I'm really unsure of how to go about calculating this problem. Any help...
Thank you everyone for the insight. I agree with quality over quantity any day. I believe the small work I have done at my university can fall within the quality category rather than quantity.
I don't expect to go to Harvard, but I owe it to myself to get somewhere reputable.
I look...
Hi There,
I am getting close to the end of my undergraduate life and am looking on to bigger and better things. Specifically, I want to attend graduate school but the program is not specified as of yet: physical chemistry, computational science, or engineering. It's all in the air at this...
Homework Statement
Find sets of all x on which the following functions are continuous
using any theorems available.
When the phrase "any thms. available" is used, we are only at a stage in my beginning analysis course where we've learned up to continuity, limits...
I'm trying to go back...
Int ((z-1)/(z+1))^n dz
If f(z) = (z-1)^(n)
Then,
Int (f(z)/(z+1)^n)
Where zo=-1
So,
2(pi)i*f^(n)(-1)/n!
For any n>0
Is this sufficient to assume? Then for whichever n is used, f(z) can be differentiated the amount of times and evaluated at (-1) as...
Homework Statement
Allow D to be the circle lz+1l=1, counterclockwise. For all positive n, compute the contour integral.
Homework Equations
int (z-1/z+1)^n dz
The Attempt at a Solution
I know to use the extension of the CIF.
Where int f(z)/(z-zo)^n+1 dz = 2(pi)i*...
Ha. I got ahead of myself and didn't even compute the integral.
(0,pi)Int(-t) dt
= -t^2/2 evaluated at (0,pi)
= -pi^2/2
Is this on the right track? Should the bounds be changed? Or is my integral entirely incorrect?
Homework Statement
Let C be the contou starting at z=-1 going around the circle lzl=1 and ending back at z=-1 (counterclockwise) determine. Int. (Log(z)/z) dz.
Homework Equations
z=e^(Log(z))
The Attempt at a Solution
So I've been stuck on this problem for quite some time...
I'm getting sum (1/5)*(5/6)^n
So,
1 = sum (1/5)*(5/6)^n
1 = (1/5) sum (5/6)^n
5 = sum (5/6)^n
5 = (5/6) + (5/6)^2 + (5/6)^3 + ... + (5/6)^n
5 = (5/6)[1 + (5/6) + (5/6)^2 +...+ (5/6)^(n-1)]
Now, I need to show this for n+1.
5 = (5/6)[1 + (5/6) + (5/6)^2 +...+...
Homework Statement
There are two separate series I'm having trouble with, although they're related.
The scenario: Roll a fair die until a six comes up.
pmf = (5/6)^(x-1) * (1/6)
So first, show the sum from 1 to infinity of p(x) =1
Next, determine P(X=1,3,5,7,...) that it will...
Well thinking about it, the exponential function is
e^z=(e^x)(e^iy)=(e^x)( cos(y)+i(sin(y)) ).
It's derivative I'm guessing is the four partial's where
u(x,y) = e^x(cos(y)) and,
v(x,y) = e^x(sin(y)).
Then ux=vy
and uy=-vx
So with this, must we turn e^iz into cos(z)+isin(z)?
Then...
Homework Statement
Show that any non-increasing bounded from below sequence is convergent to its
infimum.
Homework Equations
Not quite sure... is this a monotonic sequence?
The Attempt at a Solution
At this point I'm not even sure about which route to go. I am in need of...