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...
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...
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]
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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...
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...
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...