Joint Density of Bernoulli

Question

Let $X_1$ and $X_2$ be iid $Bern(p)$. Let $f$ be the joint density of $(X_1,X_2)$, so $f(x_1,x_2)=P(X_1=x_1,X_2=x_2)$.

What is $f(1,0)$?

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Since a bernoulli is $p$ at $1$ and $1-p$ at $0$, is $f(1,0) = p(1-p)$?

Answer 1

You would be right, specifically because of the independence of the variables. Thus when I have a joint probability, $$P(X_1 = x_1, X_2 = x_2) = P(X_1 = x_1)P(X_2 = x_2).$$