Estimating differences of independent draws

  1. Show that if \(X\) and \(Y\) are independent random variables, then
    \[\mathrm{Var}(X- Y)=\mathrm{Var}(X+Y)\]
  2. Let \(D_1\) and \(D_2\) represents two draws at random with replacement from a population, with \(\mathbf{E}D_1=10\) and \(\mathbf{SD}(D_1)_1=2\). Find a number \(c\) so that
    \[\mathbf{P}(|D_1 -D_2| < c) \geq .99\]

From [Pittman p. 203, #15]

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