In this thesis, we consider the noise properties of a Coulomb blockaded quantum dot weakly coupled to two non interacting leads. We consider two approaches to calculating the density of states of the quantum dot, the first of which uses a functional integral approach which is difficult to extend to consider the noise problem. We show that the second approach also returns the correct result for the density of states and can be extended to calculate the noise power spectrum for the interacting quantum dot. We calculate the Fano factor in the shot noise regime and evaluate numerically the Fano factor as a function of the bias voltage.