Two courses ECE 280 and ECE 980 each have sophomores juniors

Two courses, ECE 280 and ECE 980, each have sophomores, juniors, and seniors enrolled, as shown in the following table. Random variable X = x_i is used to model the class outcome of an experiment with x_1 = 1, X = x_2, and X = x_3 indicating outcomes sophomore, junior, and senior, respectively. A probability experiment consists of selecting a course, then selecting a student from the chosen course. The participants in the study are more curious about ECE 980 and select that course 80% of the time. Let so that P(B_1) = 0.2 and P(B_2) = 0.8. Determine the following quantities for the experiment: [Cauchy distribution, p.d.f., expectation, c.d.f.] A Cauchy random variable, X, has the following p.d.f. fx(x) = b/pi/b^2 + (x - a)^2, in which b is any positive real number, and a is any finite real number. Show that a Cauchy random variable has no average value. Show that the c.d.f. for a Cauchy random variable is F_X (x) = 1/2 + 1/pi tan^-1 (x - a/b).

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