Recent content by Eulogy

Homework Statement Let U,Y be independent random variables. Here U is uniformly distributed on (0,1) Where as Y~0.25\delta_{0} + 0.75\delta_{1}. Let X = UY. Find the Cdf and compute P(0≤X≤2/3) The Attempt at a Solution Normally a question like this is fairly straightforward but I'm having...

Yeah just figured it out thanks for your help!

Such a sequence could not be totally bounded since if I took a finite cover of the space with balls radius say half then each function in the sequence must be in a separate ball and as the sequence is infinite this leads to a contradiction. But I can't think of a sequence functions that are...

Homework Statement Let G = { f \in C[0,1] : ^{0}_{1}\int|f(x)|dx \leq 1 } Endowed with the metric d(f,h) = ^{0}_{1}\int|f(x)-h(x)|dx. Is G totally bounded? Prove or provide counterexample 2. Relevant Theorems Arzela-Ascoli Theorem, Theorems relating to compactness, equicontinuity etc...

I have tried this but was unable to show it was a contraction. I'm not to sure if I have the wrong integral operator for this particular question or if I'm trying to show a contraction in the wrong way.

Homework Statement For the space of continuous functions C[0,T] suppose we have the metric ρ(x,y) =sup _{t\in [0,T]}e^{-Lt}\left|x(t)-y(t)\right| for T>0, L≥0. Consider the IVP problem given by x'(t) = f(t,x(t)) for t >0, x(0) = x_{0} Where f: ℝ×ℝ→ℝ is continuous and globally Lipschitz...

Thanks guys, makes a lot more sense now!

Hi, can someone give me pointers on this question Homework Statement Prove or provide a counterexample: If f : E -> Y is continuous on a dense subset E of a metric space X, then there is a continuous function g: X -> Y such that g(z) = f(z) for all z element of E. The Attempt at a Solution...