EEET-4071 - Advanced Control and Signal Processing - Engineering Assignment Help

Assignment Task

1 Problem : Classical Estimation
Consider the following family of probability distributions
f(k; p) ≡ Pr(X = k) = (k + 1)(1 − p)kp2
where 0 < p < 1 is a parameter and k is a nonnegative integer.
1. Derive the maximum likelihood estimator pˆ for the unknown p.
2. Use Matlab to numerically compute Ep[ˆp] when p = 1/2. Show your code in your answer. Is pˆ an unbiased estimator. Justify your answer.

2 Problem : Bayes Estimation
Consider two random variables with the following probability mass function
y = 0 y = 1 y = 2
x = 0 1/8 3/8 0
x = 1 1/16 1/8 5/16
where X is the unknown to be estimated and Y is the observation.
1. Find the means X, ¯ Y¯ , the variances CX and CY and the cross covariance CXY .
2. Suppose we observe that Y = 1. What is the MMSE estimate for X.
3. Find the LMMSE estimate of X when Y = 1.
 

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