GATE Civil Engineering
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If $f(x)$ and $g(x)$ are two probability density functions,

$f(x) = \begin{cases} \frac{x}{a}+1 & :-a \leq x < 0 \\ -\frac{x}{a}+1 & : 0 \leq x \leq a  \\ 0 & :\text{otherwise} \end{cases}$

$g(x) = \begin{cases} -\frac{x}{a} & :-a \leq x < 0 \\ \frac{x}{a} & : 0 \leq x \leq a  \\ 0 & :\text{otherwise} \end{cases}$

Which one of the following statements is true?

  1. Mean of $f(x)$ and $g(x)$ are same; Variance of $f(x)$ and $g(x)$ are same
  2. Mean of $f(x)$ and $g(x)$ are same; Variance of $f(x)$ and $g(x)$ are different
  3. Mean of $f(x)$ and $g(x)$ are different; Variance of $f(x)$ and $g(x)$ are same
  4. Mean of $f(x)$ and $g(x)$ are different; Variance of $f(x)$ and $g(x)$ are different
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