Problem 1 Conditional probability Two courses ECE 280 and EC

Problem 1 [Conditional probability] Two courses, ECE 280 and EC\'E 980, each have sophomores, juniors, and seniors enrolled, as shown in the following table.Random variable X = xi is used to model the class outcome of an experiment with x1 = 1, X = x2, and X = x3 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 B1 the event \"choose ECE 280\" and B2 the event \"choose ECE 980\" , so that P(B1) = 0.2 and P(B2) = 0.8. Determine the following quantities for the experiment: P(xi|B1) and P(xi||B2) for i = 1.2,3. Fx(x|B2) for x R. fx(x|B2) for x R. P(X =xi) for i = 1,2,3.Problem 2 [Poisson distribution] The number of data packets arriving in 1 sec at a particular switch (in millions) is modeled by random variable X wliich is Poisson distributed with parameter lambda = 2. Find the probability that X = 3 million packets arrive in a given second. Find the probability that X = 0 packets arrive.

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