GATE 2016 CS – Question 14
A probability density function on the interval $[a, 1]$ is given by $1/x^2$ and outside this interval the value of the function is zero. The value of $a$ is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.49 to 0.51
Explanation
A density must integrate to 1. $\int_a^1 \frac{1}{x^2} \, dx = \left[-\frac{1}{x}\right]_a^1 = -1 + \frac{1}{a}$. Setting this equal to 1 gives $\frac{1}{a} = 2$, so $a = 0.5$.