GATE | GATE-CS-2016 (Set 1) | Question 14

A probability density function on the interval [a, 1] is given by 1 / x2 and outside this interval
the value of the function is zero. The value of a is :

Note : This question was asked as Numerical Answer Type.
(A) -1
(B) 0
(C) 1
(D) 0.5

Answer: (D)

Explanation:  \int_{a}^{1} (\frac{1}{x^{2}}) = \left [ \frac{-1}{x} \right ]_{a}^{1} = \left [ -1 + \frac{1}{a} \right ]
But, this is equal to 1.
So, (-1) + (1/a) = 1
Therefore, a = 0.5
Thus, D is the correct option.

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