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The questions for the midterm 1 of the probability and random processes course offered by the department of eecs at the university of california, berkeley in spring 2007. The exam covers various topics in probability, including the uniform distribution, poisson distribution, conditional probability, markov's inequality, and expected value and variance calculations.
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Department of EECS - University of California at Berkeley EECS 126 - Probability and Random Processes - Spring 2007 Midterm 1: 2/19/
Let X be Poisson with parameter λ > 0. For any positive integer k, calculate E(X(X − 1)(X − 2) × · · · × (X − k)).
You do not feel too well and you wonder why. The prior probability that you have the flu, some food poisoning, or some other disease D is 10%, 5%, and 15%, respectively. The probability that you feel this sick if you have the flu, food poisoning. or the disease D, is 80%, 95%, 20%, respectively. What is the probability that you are sick because of food poisoning?
Can you find a probability space and events A, B so that P [A|B] > P (A) and P [B|A] < P (B)?
Let X be a random variable that is uniform in [0, 1]. Calculate the variance of X n for n ≥ 1.
State and prove Markov’s inequality.
The random variable X has the c.p.d.f. shown above. Calculate E(X) and var(X).
