Question: 4.15. Let X be a continuous random variable with pdf / given by: f(x)-ax, -a 0 x 1, 1 x 2, =-ax + 3a, 2

4.15. Let X be a continuous random variable with pdf / given by: f(x)-ax, -a 0 x 1, 1 x 2, =-ax + 3a, 2 x 3, - 0, elsewhere.

(a) Determine the constant

(b) Determine F, the cdf, and sketch its graph.

(c) If X1, X2, and X3 are three independent observations from X, what is the prob- ability that exactly one of these three numbers is larger than 1.5?

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