Math Solutions

(Solved) Let X be a random variable with CDF F(x). Show that E((X-c)^2) is minimized by the value c = E(X). Assuming that X is continuous, show that E(|X-c|)

Question: Let X be a random variable with CDF \(F\left( x \right)\).

  1. Show that \(E\left( {{\left( X-c \right)}^{2}} \right)\) is minimized by the value c = E(X).
  2. Assuming that X is continuous, show that \(E\left( |X-c| \right)\) E[absolute value of (X-c)] is minimized if c is the median, that is, the value such that F(c) = ½.
    Price: $2.99
    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


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