Recent content by TelusPig

Oh it did turn out to be the same answer. I think I confused one of my "i"s with a "1" on paper. Thanks a lot though for the supplemental info above! :)

I tried going back to this and elaborated more, by thinking that the sum of j is just like the sum of integers formula \sum_{i=1}^n \left( \sum_{j=i+1}^{n}i +2\sum_{j=i+1}^{n}j \right) \sum_{i=1}^n \left(i(n-(i+1)+1) +2\sum_{j=1}^{n-i}(j+i) \right) by index shifting \sum_{i=1}^n...

May I ask how you are computing the "2j" sum? I'm guessing it's the 2 last terms n(n+1) - i(i+1) since (n-i)i sums the "i" term.

Homework Statement How can I compute the sum An example to calculate \sum_{i=1}^n\sum_{j=i+1}^n(i+2j)?? I only have an example where n=1 and it gives a sum of 0 (why?) Maybe with n=3, what would the expanded form look like? Homework Equations I know how to do double sums, but...

OH obviously! LOL omg, I can't believe I didn't see that and thought I had to do a bunch of integrals ._. Thanks! :D

Does that mean it's \frac{M_X''(t)M_X(t)-(M_X'(t))^2}{(M_X(t))^2} Do I have to then substitute each M(t), M'(t), M''(t) with it's integral definition then? and somehow simplify that big mess o.o?

It would be for 1st derivative: \frac{1}{f(t)}*f'(t) then differentiate again for the 2nd derivative, that would be: \frac{f''(t)f(t)-(f'(t))^2}{(f(t))^2}

Moment generating functions: How can I show that Var(X)=\frac{d^2}{dt^2}ln M_X(t)\big |_{t=0} Recall: M_X(t)=E(e^{tx})=\int_{-\infty}^{\infty}e^{tx}f(x)dx E(X^n)=\frac{d^n}{dt^n}M_X(t)\big |_{t=0} Var(X)=E(X^2)-[E(X)]^2=E[(X-E(X))^2] ------------ I tried just applying the equation...

Homework Statement If g(x)\ge 0, then for any constant ##c>0, r>0##: P(g(X)\ge c)\le \frac{E((g(X))^r)}{c^r} Homework Equations I know that E(g(X))=\int_0^\infty g(x)f(x)dx if g(x)\ge 0 where ##f(x)## is the pdf of ##X##. The Attempt at a Solution I tried following a similar...

Never mind! I finally figured it out... I had a -infinity instead. All is good :) I got k = 1/theta if anyone was interested

Ok I see what you mean. But even if I do that, the upper bound of infinity is giving me problems because e^(infinity) is infinity :S

Homework Statement Find k such that the function f(x)=ke^{-\frac{x-\mu}{\theta}} is a probability density function (pdf), for x > \mu, \mu and \theta are constant. Homework Equations The property of a pdf says that the integral of f(x) from -\infty to \infty equals 1, that is...

Well I know that having a bigger area wold mean that the denominator increases, so that the overall result is smaller, as I said in my first post "I understand from this formula that the terminal velocities would be different since objects with a higher surface area would have lower terminal...

Sorry: m = mass, g = 9.81m/s², p = density, A = projected surface area, C = drag coefficient

Why do different objects having the same mass but different projected surface areas have different terminal velocities? On wikipedia, the formula for terminal velocity is Vt = sqrt (2mg/pAC) http://en.wikipedia.org/wiki/Terminal_ve ... I understand from this formula that the terminal velocities...