If f(𝑥) and g(𝑥) are two probability density functions, f (x) = {\\begin{array}{c}\\\{x\end\frac{array}{a} + 1 , −a \leq x < 0 ; −\frac{x}{a} + 1 , 0 \leq x \leq a ; 0 , \otherwise . ; } g (x) = \{\begin{array}{c}−\\\{x\end\frac{array}{a} , : −a \leq x \leq 0 ; \frac{x}{a} , : 0 \leq x \leq a ; 0 , : \otherewise ; }. Which one of the following statements is true?

Correct Answer is : Mean of f(𝑥) and g(𝑥) are same; Variance of f(𝑥) and g(𝑥) are different

Mean of f(𝑥) and g(𝑥) are same; Variance of f(𝑥) and g(𝑥) are same

Mean of f(𝑥) and g(𝑥) are same; Variance of f(𝑥) and g(𝑥) are different

Mean of f(𝑥) and g(𝑥) are different; Variance of f(𝑥) and g(𝑥) are same

Mean of f(𝑥) and g(𝑥) are different; Variance of f(𝑥) and g(𝑥) are different

GATE Civil Engineering (CE) 2016 Shift 2 Solved Paper

Question : 37 of 65

Marks: +1, -0

If f(𝑥) and g(𝑥) are two probability density functions,

f (x) = {\{\table \;{x}/{a} + 1 , −a ≤ x < 0 ; −\;{x}/{a} + 1 , 0 ≤ x ≤ a ; 0 , \otherwise . ; }

g (x) = \{{\table −\;{x}/{a} , :\;−a ≤ x ≤ 0 ; \;{x}/{a} , :\;0 ≤ x ≤ a ; 0 , :\;\otherewise ; }.

Which one of the following statements is true?

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