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
For a Bernoulli distribution:
The Attempt at a Solution
I have that Pr(X=0)=Pr(Y=0)=2/3
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.