Consider a Gamma class conditional model for binary classification where the inputs are 1D scalars that are always greater than zero (xR+), and the output is a binary classy{0,1}

In this model it is assumed thatp(xy=c)=Gamma(xc,c) wherec andc are the parameters of the Gamma distribution ofx for classc and that p(y)=Bernoulli(y).

The probability density function of the Gamma Distribution is: Z(,)x1exp(x), whereZ(,) is the normalization constant which doesn't depend on x. Derive the function whose zeros (points where the function is equal to zero) define the decision boundary between the two classes for this model.

For the cases when either0=1 or0=1 give direct expressions for the values ofx which lie on the decision boundary. What is the geometric structure of the decision boundary for this model and why? What is the decision boundary if both0=1 and0=1