Question: Let X have the density f(x) = Cx for 0 x 1,f(x) = C(2 x)/2 for 1 < x 2, and

Let X have the density f(x) = Cx for 0 ≤ x ≤ 1,f(x) = C(2 − x)/2 for 1 < x ≤ 2, and f(x)=0 otherwise. Find C and F(x). Compute the following probabilities and show them on the graphs of f(x) and F(x): (i) P(X ≥ 3/2). (ii) P(|X − 1| ≤ 1/2).

(Hint: The problem can be solved without integration, just using simple geometry.)

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