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  1. E

    Probability Spaces

    Homework Statement Let \Omega = [0,1) Let G be the collection of all subsets of \Omega of the form [a1,b1),\cup[a2,b2),\cup...\cup[ar,br) For r any non-negative integer and 0<=a1 and a1 <=b1 <= a2 .... Show that G is a field Show that G is not a \sigma-field Homework...
  2. E

    Determine whether the following series converges

    Homework Statement Determine whether the following series converges: \sum \frac{(n-1)^3}{\sqrt{n^8+n+2}} Homework Equations Definition of convergence: Let \sum a_{n} be a series. If the sequence of (sn) partial sums converges to L (finite). Then we say the series converges to L or has...
  3. E

    Partial derivative of an Integral

    Homework Statement Show \partial /\partial u \int_{a}^{u} f(x,v) dx = f(u,v) Homework Equations The Attempt at a Solution Basically i understand that we hold all other variables constant, and i understand that we will get our answers as a function of u and v. But to show that we have...