Recent content by Zone Ranger

assume P(A|B')>P(A) then \frac{P(A\cap B')}{P(B')}>P(A) \frac{P(B'|A)P(A)}{P(B')}>P(A) \frac{P(B'|A)}{P(B')}>1 P(B'|A)>P(B') 1-P(B'|A)<1-P(B') P(B|A)<P(B) the other one isn't much different

I assume you want \int_{-\infty}^t x(\tau)d\tau-\int_{-\infty}^{t-T} x(\tau)d\tau=\int_{-\infty}^t [x(\tau)- x(\tau-T)]d\tau from where you are stuck...let s=\tau and combine the integrals

The book is correct. You need to sum over y. f_X(x)=\sum_{y=1}^3f_{X,Y}(x,y)=\sum_{y=1}^3\frac{1}{36}xy=\frac{1}{36}x(1+2+3)=\frac{x}{6} Edit: I just noticed that you do have the correct answer. Think about it.

1\geq P(A\cup B)=P(A)+P(B)-P(A\cap B) 1\geq x+y-P(A\cap B) P(A\cap B)\geq x+y-1 \frac{P(A\cap B)}{P(B)}\geq \frac{x+y-1}{y} P(A|B)\geq \frac{y-(1-x)}{y} P(A|B)\geq 1-\frac{1-x}{y}

let \mathcal{F} be a sigma algebra over a set \Omega since \mathcal{F} in noempty there exists an A\in\mathcal{F} since \mathcal{F} is a sigma algebra A^c\in\mathcal{F} and A\bigcup A^c=\Omega\in\mathcal{F}

I didn't find what i am looking for in the link you provided. I'm looking for a general chenistry book in pdf format. I can find a lot of math books... http://directory.google.com/Top/Science/Math/Publications/Online_Texts/ but I can't find any chemistry books.

I'm looking for a general chemistry book online in pdf format. I can't seem to find one. could someone help me. -thanks

http://en.wikipedia.org/wiki/Variance Read the section "Population variance and sample variance"

X_n does converge in mean square to X (X=0) the expected value of (X_n-X)^2 goes to 0 as {n \to \infty }.

a.s.=Almost surely http://www.answers.com/topic/convergence-of-random-variables

the X_n have to be random variables (measurable functions). you are correct that for your choice of X_n, X_n(0)>0. but still X_n->0 a.s. so with your X_n (2) still holds.

let X_1 =1 on [0,1] let X_2=1 on [0,1/2] , 0 otherwise let x_3=1 on [1/2,1] , 0 ow let x_4=1 on[0,1/3] ,0 ow let x_5=1 on [1/3,2/3] , 0 ow ... can you show that X_n converges in probability (1) but x_n does not converge a.s. (2)

look at the first quadrant. assume x<y then set \sqrt{x^2+y^2}=s-y. solving for y we get y=\frac{s^2-x^2}{2s} find out what x ranges over (find out when x=y). so take y=\frac{s^2-x^2}{2s} and replace y by x to get x=\frac{s^2-x^2}{2s}. solve for x you get (\sqrt{2}-1)s so then...

i used MATLAB to run 10,000 simulated dart throwings. i got p=.2193. which is close to the theoretical value i got.

I get \frac{4\sqrt{2}-5}{3}\thickapprox .21895