Let X and P be independent and uniformly distributed on [-1, 1]. Given the following facts: E[X] = E[X^3] = E[X^5] = 0 E[X^2] = 1/3 E[X^4] = 1/5 Suppose that Y = X^3 + P 1. Find the LMS estimate of Y, given that X = x. (Notice we are trying to estimate Y from X, not the opposite direction, and your answer should be a function of x.) 2. Find the LLMS estimate for Y, given that X = x. (Your answer should be a function of x.)

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