A probability density function on the interval [1/e^2, 1] is given by f(x) = a/x, and outside this interval the value of...

Question

A probability density function on the interval [1/e^2, 1] is given by f(x) = a/x, and outside this interval the value of the function is zero. The value of a is ___________.

Accepted Answer

0.5 A valid probability density function must integrate to 1 over its entire support. The function f(x) = a/x is defined on [1/e^2, 1]. We integrate f(x) over this interval and set the result equal to 1 to find the constant a. The integral of 1/x is ln(x), so evaluating between the limits gives the value of a.