def update_theta(self, X, R):
        """Compute the update for the Bernoulli parameters in the M-step of the E-M algorithm.
        You should derive the optimal value of theta (the one which maximizes the expected log
        probability) by setting the partial derivatives to zero. You should implement this in
        terms of NumPy matrix and vector operations, rather than a for loop."""

        ######################## Your code here #########################
        a = self.prior.a_pixels
        b = self.prior.b_pixels
        sumR = np.sum(R, axis=0) + (a-b) # sum over all examples (e.g. sum columns)
        RprimeX = np.dot(R.transpose(),X) + a - 1
        # in numpy, elements of column 0 are divided by the divisor's element 0.
        # we want each row to be divided by the same number
        # so we transpose so that rows become columns, do the division, then transpose back
        theta = np.true_divide(RprimeX.transpose(), sumR).transpose()
        return theta