Recent content by roadworx

Hi, I have: \frac{a}{b+a+s} + \frac{c*b}{(b+a+s)(c+s)} I can rearrange that to: \frac{a-c}{b+a-c} * \frac{b+a}{b+a+s} + \frac{b}{b+a-c} * \frac{c}{c+s} Is this correct? If so, can someone tell me why the +s changes into a -c?

So Prob(P<p/x) = p/x -1 ? when p=x Prob = 0, and 2p = x, Prob = 1 So xP still follows a Uniform Distribution ~ U(1, 2). It looks as though I've assumed this though.

If I have random variable, P ~ U(1,2), am I correct in thinking that xP ~ U(1,2) also ? (where x is some constant), or does the range change? Thanks.

Basically this is what I've got. \int_0^{inf} 2 \theta^{-2}x^{3+2m} dx Using y=x^2 / \theta, if I rearrange this I get somehow: \int_0^{inf} \theta^{m}y^{m+1} dy Does anyone know where the final x in x^{3+2m} disappears to?

Hi, I'm trying to use moments to find the mean of a pdf. Here is the pdf: f(x|\theta) = 2 \theta^{-2}x^3 exp(\frac{-x^2}{\theta}) I'm not really sure where to start. I can multiply the pdf by X and then integrate with respect to X, but it gives me the wrong answer. Any ideas...

Hi, I have a question on stationarity in time series. I basically understand the concept, I think. However, I don't understand why the lag should affect the joint distribution. For example, the joint distribution of <Yt, Yt+a> should be the same as the joint distribution of <Yp...

hi, I have: exp \left(-\frac{\lambda}{2^\mu^2} \sum_{i=1}^n \frac{(x_i-\mu)^2}{x_i}\right) I am trying to work out why this simplifies to: exp\left(\frac{n \lambda}{\mu}\right) exp \left( -\frac{\lambda}{2^\mu^2} \sum_{i=1}^n x_i -\frac{ \lambda}{2} \sum_{i=1}^n \frac{1}{x_i}...

Can anyone give me an example of when a statistic is insufficient, using the factorization theorem, if possible? Thanks.

Hi, I have the following equation \gamma_0 = \phi^2 \gamma_0 + (1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2 The answer is \gamma_0 = \frac{(1 + 2\Theta\phi+\Theta^2)}{1-\phi^2} I get how to factorize the numerator. I'm not sure of the denominator. It looks like a geometric...

Thanks for that. I have a question on your reparameterization. Isn't \varphi^{\kappa} to the negative index, and therefore shouldn't it be \frac{1}{\varphi^{\kappa}} when you write out the series? Or did I miss something?

Hi, I have \sum_{j=\kappa}^{\inf} \varphi^{2j-\kappa}\sigma^2 I know the answer is = \frac{\sigma^2}{1-\sigma^2} \varphi^\kappa Can someone explain the mathematics involved in this derivation? Thanks.

hi, I have a question on determining whether rectangular matrices are singular. \left[1 0 0 1 0\right] \left[1 0 0 0 1\right] \left[0 1 0 1 0\right] \left[0 1 0 0 1\right] \left[0 0 1 1 0\right] \left[0 0 1 0 1\right] The book says it's singular. But the explanation isn't very...

Hi, I'm trying to find the derivative of -ln(-\Theta) with respect to \Theta The answer's -\frac{1}{\Theta} I'm not sure why though. Here's my working. \frac{d}{d\Theta} -ln(-\Theta) = \frac{d}{d\Theta} ln(-\frac{1}{\Theta}) = -\Theta Can anyone explain where I'm...

Hi, I have the following equation: \Theta = log \left(\frac{\Pi}{1-\Pi}\right) I want to re-arrange it for \Pi Here's my attempt: \Theta = log \left( \frac{\Pi}{1-\Pi}\right) \Theta = log \left( \Pi \right) - log \left(1-\Pi \right) exp^{\Theta} = \Pi - (1-\Pi)...

Hi, Can anyone derive the sum of exponentially distributed random variables? I have the derivation, but I'm confused about a number of steps in the derivation. Here they are: Random variable x has the PDF, f(s) = \left\{ \begin{array}{c l} e^{-s} & if s \ge 0 \\ 0 &...