1. The problem statement, all variables and given/known data Take Ω = [0, 1] and P the uniform probability. (a) Give an example of two random variables X and Y deﬁned on Ω that both have the same Bernoulli distribution with parameter θ = 1/3. (b) Give an example of such random variables that are independent, and not independent. 2. Relevant equations For a Bernoulli distribution: Pr(x=0)= 1-θ Pr(x=1)= θ 3. The attempt at a solution I have that Pr(X=0)=Pr(Y=0)=2/3 Pr(X=1)=Pr(Y=1)=1/3 What I am not sure about is the part where I am asked for the examples of 2 random variables with this distribution. Can I simply say let X represent the chance of rolling a 1 on a 3 sided dice as an example? Then what would I choose for Y such that X and Y are independent for the second part? Thanks for your help.