TASK 1: INTEGRATION Another application of integration is in probability. This task applies your algebra and calculus skills to this domain. If X is a continuous random variable with range [a, b] then the probability density function satisfies the following two properties: Property 1: f(x) 2 0 for all x E [a, b]. Property 2: f(x) dx = 1. a Question 1 (1) Explain why the following functions are, or are not, probability density functions: (a) f(x) = > for a E [1, e0.5] (b) f(x) = (16 - 24) for a E [0, 4] (c) f(x) = 3 sin(x) for x E [0, 57]