The document discusses demonstrating that the function f(x) = x^2/2 is a probability density function for a random variable x over the interval [1, ∞). It also involves calculating the probability p(1 < x < 2).

1. 10. Show that the function f ( x ) = x 2 2 is a probability density function for a random variable X
over the interval [ 1 , ) . Find the probability P ( 1 X < 2 ) .