# Logistic Regression Maximum Likelihood

Is it true that we assume our P(y|x;theta) to follow Bernoulli's distribution given y has binary output in Logistic Regression? Is there any specific reason why we consider Bernoulli's distribution?

If 1) is true., What happens if we consider P(y|x; theta ) as Gaussian distribution? What would be our cost function? I mean if we assume Gaussian, we can have optimal value of mean and variance by taking mean of (y|x) and its variance which is what we are maximizing the likelihood for.