Recent content by covariance64

  1. C

    Prove Convergence of Integral (1/x)sin(1/x)dx from 0 to 1

    Homework Statement Show that the integral of (1/x)sin(1/x)dx from 0 to 1 is converges absolutely? Homework Equations The Attempt at a Solution Should we use the comparison test in this situation?
  2. C

    Graduate Conditional expectation and variance

    I have found that E[X|Z=1] = E[X|X<Y] = 1/9 E[X|Z=0] = E[X|X>Y] = 8/9 by integrating, and conditioning on the random variable Y. So E(X) = E(E(X|Z)) = (1/9)(1/3) + (8/9)(2/3) = 17/27, which contradicts the fact that E(X) = 1, for X exponential with mean 1. I am wondering where is...
  3. C

    Graduate Conditional expectation and variance

    Let X, Y be independent exponential random variables with means 1 and 2 respectively. Let Z = 1, if X < Y Z = 0, otherwise Find E(X|Z) and V(X|Z). We should first find E(X|Z=z) E(X|Z=z) = integral (from 0 to inf) of xf(x|z). However, how do we find f(x|z) ?