- #1
cutesteph
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Homework Statement
What is the expected value of ||Ax+n|| where || || is the L2 norm and x and n are uncorrelated and E[n] = 0
The Attempt at a Solution
E[ norm of Y] = E[(Ax+n)' (Ax+n)] = E[(x'A'+n')(Ax+n)] = E[x'A'xA +x'T'n +n'Ax +n'n]
the three last terms = 0 due to uncorrelatedness so = E[x'A'xA] = E[tr(x'A'xA)] = E[tr(x'xA'A)] = A'AE[x'x] does this reduce any further?