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Problem 2 (35 Points) In a bag, there are 7 balls with 3 being red, 2 being yellow, 2 being blue. Randomly pick 3 balls from the bag without replacement. Denote the number of red balls picked as a random variable X and the number of yellow balls picked as a random variable Y, respectively. 1. (5 Points) Find the (discrete) joint probability distribution function p(r, y) of X and Y. ATTENTION: You MUST use a closed-form expression here using combination, permutation, and/or factorial numbers and DO NOT just list the probabilities. 2. (5 Points) Find the effective domain of this joint pdf, namely, the sample space of this bivariate random variable (X, Y). 3. (10 Points) Find the marginal probability functions px (x) for X and py(y) for Y, respectively. 4. (10 Points) Find the conditional probability functions pxx (xly)- ATTENTION: In this part, you can list the values of this function for all possible inputs (xly). 5. (5 Points) Use the result in part 4 to find the conditional expectation E( X Y = 1)