## Question

# Consider k measurements that are corrupted by zero-mean Gaussian noise with s.d. , i.e., z=x+wi, i = 1,..., k (6) where x is a

Consider k measurements that are corrupted by zero-mean Gaussian noise with s.d. , i.e., z=x+wi, i = 1,..., k (6) where x is a constant and w; ~N(0,0). The goal is to estimate the mean x and the variance of the data and analyze the characteristics of the estimation through the following steps. First, let us denote the entire data as z = {21, 22, ..., zk}. 1. Write the likelihood function A(x, 0) = p(zk|x, 0) 2. Find ML the ML estimate of x 3. Find L, the ML estimate of the variance 4. Find E (ML). 5. Find E (L)

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