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Say $x_1$ and $x_2$ are normal random variables with known means and standard deviations and $C$ is a constant. If $y = \max(x_1,x_2,C)$, what is $\mathrm{Var}(y)$?

Well, I forgot to tell that $x_1$ and $x_2$ are independent.

  • 1
    You need to know the _joint_ distribution function of $X_1$ and $X_2$. Are they given to be _independent_ but you neglected to tell us so?2012-07-30
  • 0
    Presumably the $x_i$ are independent?2012-07-30
  • 3
    Answer: a complicated function of $C$ and of the means and standard deviations of $x_1$ and $x_2$.2012-07-30

3 Answers 3