The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=(x-1)²(4-x) for 1 ≤ x ≤ 4 and 0 otherwise. a) What is the probability that X > 2.5?¹ b) What is the probability that X < 2.572 c) What is the probability that 1.25 < X < 2.75? d) What is the expected value of X? 4 e) What is the expected value of X-3? 6 f) What is the expected value of 3X? 9) What is the expected value of x27 h) What is the probability that X is less than its expected value? 8

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