GATE Papers >> Civil >> 2017 >> Question No 26

Question No. 26 Civil | GATE 2017

For the function $\style{font-family:'Times New Roman'}{f(x)=a+bx,\;0\leq x\leq1}$, to be a valid probability density function , which one of the following statements is correct?


Answer : (B) = 0.5, = 1


Solution of Question No 26 of GATE 2017 Civil Paper

For probability density function = f(x) to be

valid $\int_{-\infty}^\infty f(x)=1$

$\begin{array}{l}\int_{-\infty}^\infty\mathrm a+\mathrm{bx}=1\\\int_0^,(\mathrm a+\mathrm{bx})\mathrm{dx}=1\\\mathrm{ax}+\frac{\mathrm{bx}^2}2\rbrack_0^1=1\\\mathrm a+\frac{\mathrm b}2=1\end{array}$

for equation to be satisfied a = 0.5  b = 1

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