Unformatted text preview: e ) [6 pt] Problem 2. 1. If X is a random variable with variance σ 2 and a is a deterministic scalar, determine the variance of aX . [6 pt] 2. If X is a random vector with covariance matrix Σ and A is a deterministic matrix of appropriate dimension, determine the covariance matrix of A X . [8 pt] Problem 3. Let X be a random variable whose pdf is given by f X ( x | θ ) = ( 2 θ 2 x < x < θ otherwise Suppose a single observation x o of X is given (assume x o > 0). 1. What is the likelihood function ‘ ( θ | x o )? [7 pt] 2. Provide a sketch of ‘ ( θ | x o ). [7 pt] 3. Find the max-likelihood estimator of the parameter θ given the single observation x o . [6 pt] Prabir Barooah 1...
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- Fall '08
- Probability theory, probability density function, Cumulative distribution function, Prabir Barooah, Aerospace Engineering Instructor