Change of Variable: Gaussian

Let \(Z\)  be a standard Normal random variable (ie with distribution \(N(0,1)\)). Find the formula for the density of each of the following random variables.

  1. 3Z+5
  2. \(|Z|\)
  3. \(Z^2\)
  4. \(\frac1Z\)
  5. \(\frac1{Z^2}\)

[based on Pitman p. 310, #10]

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