Q78
If f(x) and g(x) are two probability density functions, \[ f ( x ) = \ array*20c x a + 1&:& - a x < 0 \\ - x a + 1&:&0 x a \\ 0&:& otherwise array .;\,\, g ( x ) = \ array*20c - x a&:& - a x < 0 \\ x a&:&0 x a \\ 0&:& otherwise array .\] Which one of the following statements is true?
If f(x) and g(x) are two probability density functions,
{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\text{x}}}{{\text{a}}} + 1}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ { - \frac{{\text{x}}}{{\text{a}}} + 1}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.;\,\,{\text{g}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - \frac{{\text{x}}}{{\text{a}}}}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ {\frac{{\text{x}}}{{\text{a}}}}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.
Which one of the following statements is true?
{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\text{x}}}{{\text{a}}} + 1}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ { - \frac{{\text{x}}}{{\text{a}}} + 1}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.;\,\,{\text{g}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - \frac{{\text{x}}}{{\text{a}}}}&:&{ - {\text{a}} \leqslant {\text{x}} < 0} \\ {\frac{{\text{x}}}{{\text{a}}}}&:&{0 \leqslant {\text{x}} \leqslant {\text{a}}} \\ 0&:&{{\text{otherwise}}} \end{array}} \right.
Which one of the following statements is true?
A.
Mean of f(x) and g(x) are same; Variance of f(x) and g(x) are same
B.
Mean of f(x) and g(x) are same; Variance of f(x) and g(x) are different
AnswerC.
Mean of f(x) and g(x) are different; Variance of f(x) and g(x) are same
D.
Mean of f(x) and g(x) are different; Variance of f(x) and g(x) are different
Answer: Option B
Solution
Answer: Option B
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