Recent content by Lily@pie

Sorry, my bad... I've edited it...

Homework Statement Prove the following a>0, X is a non-negative function Ʃ_{n\in N} P(X>an)≥\frac{1}{a}(E[X]-a) Ʃ_{n\in N} P(X>an)≤\frac{E[X]}{a} The Attempt at a Solution I know that \sum_{n\in N} P(X>an)=\sum_{k \in N} kP((k+1)a≥X>ka)=\sum_{k \in N} E[k1_{[(k+1)a,ka)}(X)]...

I saw this example... Ω=N P(ω)=2-ω, ω in Ω Xn(ω)=2nδω,n I can see that Xn is not convergent. But I'm not quite sure in computing the integrals... I'm very bad with the lim inf concept >_< So, I have written my attempt on evaluating the integrals and reasoning that I've used. My...

Homework Statement Let a probability space be (Ω, \epsilon, P). A set of random variables X1,...,Xn Give an example where I_{p}(lim inf_{n -> ∞}X_{n}) < lim inf_{n -> ∞}I_{p}(X_{n}) The attempt at a solution I know that I_{p}(lim inf_{n -> ∞}X_{n})=E[lim inf_{n -> ∞}X_{n}] and...

I get the second part now. This is what I was thinking for the first part, Let A={{x}:x\in ℝ} For the first part, I am trying to prove that G \subseteq σ(A) If F \in G, F is countable or the complement is countable, If F is countable, we can write F as \stackrel{\bigcup}{x\in...

To prove that G is a sigma algebra, I just showed that G satisfy the 3 axioms of sigma algebra. I admit the middle part is strange as I am not sure. I've tried the following to prove G = σ({{x}:x\in ℝ}) 1st, I will prove that G \subset σ({{x}:x\in ℝ}). Since an element in G is either...

I could prove that G is a sigma algebra. However, I'm not quite sure in proving G=σ(singletons) Can I say G \subseteq {{x}:x\in ℝ}? Then G=σ(G) \subseteq σ({{x}:x\in ℝ}). I could also show {{x}:x\in ℝ} \subseteq σ(G) Hence, G=σ({{x}:x\in ℝ}. Therefore to show σ( E_{1}) not...

Homework Statement { E }_{ 1 }:=\{ \left( -\infty ,x \right) :x\in \Re \} { E }_{ 2 }:=\{ \left\{ x \right\} :x\in \Re \} Prove \sigma \left( { E }_{ 1 } \right) =\sigma \left( { E }_{ 2 } \right) Homework Equations I know { E }_{ 1 } generates the Borel field (i.e.)...

Oh ya... I didn't notice that. I thought that it didn't make sense cz as z>>L, E should be approximately a point charge as you said. But I couldn't find anything wrong with the calculation. Will it be possible to help?? Thanks

Oh! I have solved it again and I did a mistake on the integration. So sorry and thank you! =D

Oh, my bad... the d\vec{E} is a typo and it is in the vertical direction I am pretty sure the integration is correct. Initially the z3 in the numerator does cancel off, but the integration gives out another z in the equation. Hence, I end up getting the same solution. :cry:

Homework Statement Find the Electric field at distance z above the mid point of a length L straight line segment, carrying a non-uniform line charge \lambda = \frac{1}{C} |x| where C is a constant 2. The attempt at a solution I note that the horizontal component cancels out...

I was thinking about measuring the distance between two points with the euclidean distance between the points?

So how should I go about defining it on the unit sphere??

I asked my lecturer on this solution, but he say the metric should be something that is defined along the unit sphere... Not quite what we do here...