Hi all, I’m stuck on where to begin. For the question below, my approach is simply to substitute the [imath]S_k (hat) [/imath] into the MSE formula, get an expression in terms of [imath] c_0 [/imath] and take the derivative and setting it to 0 to find the min [imath] c_0 [/imath]. I guess that is where I’m stuck in that I have the MSE in terms of expectations. If I substitute [imath]S_k (hat) [/imath] into the formula and distribute terms, I get [imath]MSE = (c_0)^2E(X_k^2) - 2c_0E(X_kS_k) + E(S_k^2) [/imath] so I’m struggling to find of those expectations. The [imath] S_k [/imath] are iid Gaussian with mean 1 and variance 1, but when I try to calculate, say, [imath] E(X_k) [/imath] , I get 0 since all [imath] S_k [/imath] are independent. That doesn’t help much, so I guess my other issue is finding [imath]E(X_k^2)[/imath], [imath]E(X_kS_k)[/imath], [imath]E(S_k^2)[/imath] etc.
Any help would be much appreciated, thank you.
Any help would be much appreciated, thank you.
Last edited: