EE 278 Midterm: EE278 Midterm Exam Fall 2017 Solutions
9 Jan 2019
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Ee278 midterm exam solutions: short questions (27 points), (3 points) assume that you are able to sample a random variable x from an exponential distribution with parameter 1 (fx(x) = e x for x 0). What is the variance of y = ef (x): (2 points) you bump into a student in the main quad. Set y1 = z and y2 = xz. Prove this is a covariance matrix by describing a construction of an n dimensional random vector with covariance matrix . Prove is a covariance matrix by describing a construction of an n dimensional random vector with covariance matrix . Hint: start with n + 1 iid zero mean, unit variance random variables. There are several options to generate the desired random variable y . Possibly the simplest one is to look for a threshold t such that x > t has probability e 2. P(x > t) = e t this threshold is equal to 2.
