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) ≥ 0 for all x € [a, b]. Property 2: [s a f(x) dx = 1. Question 1 (1) Explain why the following functions are, or are not, probability density functions: (a) f(x) = ² for x = [1, √e] (b) f(x) = 5 (9x² - x4) for x = [0, 3] 1

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