Please show all work so I can learn <3 XOXO I would appreciate it alot 😉 1 Random Variables Consider the probability space (2, A, P) defined as follows: .A-2. i.e., the event space is the power set of _; P(R)1/3, P(G) P(B) PY-2/9, where we define the probability only for the clementary outcomes, and the probability of every event in A can be deduced from these valucs (as per discussion in section A.5) This probability space can model, for example, the outcome of rolling a four-sided die whose faces are red, green, blue, and yellow. The outcome of the experiment is the color of the downward face. Next, let us consider the function X : _ R defined as follows: x(R)-2;X(G)--2;x(B) x(Y). 1. Prove that X delines a randon variable over the given probability space 2. Compute the cumulative function of Xx variable over the given probahility spaoe
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