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# Suppose we have two noisy observations y[0] = x[0] + w[0] y[1] =x[1] +w[1] where xin]; n-0, is a unknown constant, and where wO] and w[1] are statistically independ...

## Question

###### Suppose we have two noisy observations y[0] = x[0] + w[0] y[1] =x[1] +w[1] where xin]; n-0, is a unknown constant, and where wO] and w[1] are statistically independent Gaussian random variables. Assume, w[O]~N(0,1)N(0,1) if x[1] 2 0 w[1]~ N(0,2) if x[1] < 0.Consider the estimatorsx[0] = (1/2) (y[0] y[1])x[1] = (2/3) y[0] (1/3) y[1]Calculate the Cramer-Rao bound for unbiased estimation of xin] based on [y[0J] observation of Ly[1]lShow that a minimum variance unbiased estimator does not exist:

Suppose we have two noisy observations y[0] = x[0] + w[0] y[1] =x[1] +w[1] where xin]; n-0, is a unknown constant, and where wO] and w[1] are statistically independent Gaussian random variables. Assume, w[O]~N(0,1) N(0,1) if x[1] 2 0 w[1]~ N(0,2) if x[1] < 0. Consider the estimators x[0] = (1/2) (y[0] y[1]) x[1] = (2/3) y[0] (1/3) y[1] Calculate the Cramer-Rao bound for unbiased estimation of xin] based on [y[0J] observation of Ly[1]l Show that a minimum variance unbiased estimator does not exist:

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