Question: Let X be a random variable uniform over the interval [2,12]. Suppose we observe X with some random error N which isuniformly distributed over interval

Let X be a random variable uniform over the interval [2,12]. Suppose we observe X with some random error N which isuniformly distributed over interval [0,1] and independent of X. i.e.,Y = X +N

1. Find the Least mean square estimate of X based on the observation Y = y.

2. Find the mean square error

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