# Probabilistic homework problem?

I have a problem with the following homeworks:

Question1) Consider a hypothesis $h$ that makes an error with probability $\mu$ in approximating a deterministic target function $f$ (both $h$ and $f$ are binary functions). If we use the same $h$ to approximate a noisy version of $f$ given by:

$P(y\:|\:x) = \left\{ \begin{array}{ll} \lambda & y = f(x) \\ 1-\lambda & y \neq f(x)\\ \end{array} \right.$

What is the probability of error that $h$ makes in approximating $y\;$? Hint: Two wrongs can make a right!

a)$\mu\;$ b)$\lambda\;$ c)$1-\mu\;$ d)$(1-\lambda)*\mu + \lambda*(1-\mu)\;$ e)$(1-\lambda)*(1-\mu) + \lambda*\mu$

Question2) At what values of $\lambda$ will the performance of $h$ be independent of $\mu\;?$

a)$0\;$ b)$0.5\;$ c)$1/\sqrt{2}\;$ d)$1\;$ e)No values of $\lambda$

Can someone help me with these questions? I'm not really sure where to start :S

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