Recent content by Oxymoron

Note: By "somehow" I mean Gram-Schmidt.

Hi Ben, So are you saying that the metric tensor G defined between tangent spaces T_x M makes them inner product spaces (which gives you angles and lengths), and then this somehow picks out an orthonormal frame fibre E? Then, since we have the metric to preserve the inner product (and so we can...

I don't understand the geometry of what happens when you give a manifold a metric, in particular how the group structure reduces to the orthogonal group. I've read the wikipedia article http://en.wikipedia.org/wiki/Reduction_of_the_structure_group a dozen times but I get stuck when it says that...

Hi Stephen. Good idea with the conditional probability distribution. Turns out you can derive a formula for the conditional bivariate (because I am considering only 2 stocks) normal density by dividing the bivariate normal density by one of the marginals. Then you can extract the conditional...

Yes it does. Thank you micromass, I should be able to go on and calculate the expected value and variance of this pdf.

Homework Statement If the returns on two stock are jointly normal and let's say I know the means, variances (and therefore standard deviations), and correlation of each and both. Then if I know the return of one of the stocks over some time period, then would it be possible to calculate the...

I also tried using the theorem and got the same answer. What about the expected value? By definition: E[Y] = \int_{-\infty}^{\infty}y\frac{1}{2\sqrt{y}}\mbox{d}y = \infty But can I change the limits to 0 and 1 so that E[Y] = \int_0^1y\frac{1}{2\sqrt{y}}\mbox{d}y = \frac{1}{3} is this...

Okay, so when I differentiate I get f_Y(y) = \frac{\mbox{d}}{\mbox{d}y}F_Y(y) = \frac{\mbox{d}}{\mbox{d}y}F_X(\sqrt{y})\cdot\frac{1}{2\sqrt{y}}-\frac{\mbox{d}}{\mbox{d}y}F_X(-\sqrt{y})\cdot\frac{1}{-2\sqrt{y}} =f_X(\sqrt{y})\cdot\frac{1}{2\sqrt{y}}-f_X(-\sqrt{y})\cdot\frac{1}{-2\sqrt{y}}...

Homework Statement A random variable X is distributed uniformly on [-1,1]. Find the distribution of X^2, its mean and variance. The Attempt at a Solution Define a transformation of random variable as Y=X^2. Problem is that the transformation function is not monotonic on the range. If it...

Solved. I used the cumulative distribution function for Poisson: F(t,\lambda) = \frac{\Gamma\left(\lfloor k+1 \rfloor,\lambda\right)}{\lfloor k \rfloor!} and used the incomplete gamma function \Gamma(k,x) = \int_x^{\infty}t^{k-1}e^t\mbox{d}t and integrated by parts twice (twice because the...

Homework Statement If X is a Poisson random variable with \lambda = 2 find the probability that X>0.5. Homework Equations The Poisson PDF: P(x,\lambda) = \frac{\lambda^k}{k!}e^{-\lambda} The Attempt at a Solution Usually with these sorts of probability problems where they ask...

Homework Statement If a bank issues a mortgage to a borrower, let's say that it was for $P, for t years with an annual interest rate i% compounded monthly. Then, to the bank, can this essentially be treated like a bond with price $P, coupon rate i% and maturity t years? It could be...

I'm pretty sure I can find an n\in\mathbb{Z} such that |n| < 1.

You can't get a sum of 10 and a sum of 11 in a single event. So you would need at least 2 trials before you can get this. For example, if n is the number of trials then when n=1, P(A)=0. So you need to consider a sequence of trials which I think is where Roni1985 is getting his infinite series from.

Yeah okay, so it is 'and'. That makes it more difficult. I am also learning probability at the moment so I should have made that clear. Do you think it might be possible to use a probability distrbution? I had a look at your infinite sum but it is not clear to me how you came to that...