Recent content by muso07

Homework Statement Random variable U is continuous uniform in the time interval (0,2) T|U (T given U) is modeled by the mgf \frac{1}{1-ut} Find: a) E(U) b) E(T|U) and Var(T|U) c) E(T) and Var(T) Homework Equations The Attempt at a Solution a) This one was fine, E(U)=1 b) I...

Can anyone even point me in the right direction?

Whoops, that's meant to be integral from a to b for the first one and 0 to b-a for the second one.

Homework Statement Derive a formula of the form \int\stackrel{b}{a}f(x)dx \approx c_{0}f(a)+c_{1}f(b)+c_{2}f'(a)+c_{3}f'(b) that is exact for polynomials of the highest degree possible. Apply a change of variable: y=x-a Homework Equations The Attempt at a Solution I don't get the "highest...

I only read the first page of this, so forgive me if I'm repeating what someone else said, but I agree that there is a "ceiling". I was really good at maths in high school, but KNEW my level of knowledge and talent was nowhere near the kids at the top. I stupidly decided to major in maths at...

First integrate it, then you get [-e-x] from 0 to infinity. The key is to find the limit as x approaches infinity of (-e-x). (Hint: Put in a very large negative value for x and see what you get.)

Homework Statement Show that: (\stackrel{n}{k})=\#\left\{(\omega_{1},..., \omega_{n})\in\left\{0,1\right\}^{n}:\Sigma^{n}_{l=1}\omega_{l}=k\right\} (edit: the sigma is meant to go from l=1 to n) Homework Equations It says to use this...

Nevermind, I'm just going to tell him to believe me and it shall be great. Thanks for all your help!

You beat me to replying. Is the sum (1+x)/(1-x)^2?

Hm, the kid's in Year 11 so he hasn't done integration yet... But when you integrate, you get x^n. Then lim_{(a\rightarrow\infty)} [x^{n}]^{a}_{1}= lim_{(a\rightarrow\infty)}x^{a}-x=-x This isn't right, though... I feel like such an idiot. :P

Homework Statement Figuring out an infinite sum question for the kid I tutor... it's late and my brain's not functioning well. I think I'm overcomplicating the question, but I can't figure it out. The the sum of the following infinite series: S = 1+3x+5x^2+... Homework Equations The...

Okay, so I came up with something that seems wrong, but can someone tell me if it holds? Z^{-1}(\hat{F})=X^{-1}(Y^{-1}(\hat{F})) =X^{-1}(({\tilde{\omega}\in\tilde{\Omega}:Y(\tilde{\omega})\in\hat{F})) =(\omega\in\Omega:X(\omega)\in\tilde{F})\in F =(\omega\in\Omega:Z(\omega)\in\hat{F})\inF...

Homework Statement I have to prove that compositions of measurable mappings are measurable. i.e. If X is F/\widetilde{F} measurable and Y is \widetilde{F}/\widehat{F} measurable, then Z:=YoX:\Omega\rightarrow\widehat{\Omega} is F/\widehat{F} measurable. Homework Equations X is...

That's exactly right. :)

Have you had a go at this? First of all you need to find equations for your problems, and from there differentiate them to find the maximum/minimum. If you have a go at the problems, I'll help you some more.