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Presume we have two independent binomial random variables that both have success probability in a single trial of p. The random variable X denotes the number of successes in three trials, whereas the random variable Y represents the number of successes in two trials. We form a new random variable Z = X + Y.
1. What is the expected value of Z?
2. What is its probability distribution of Z?
Create and explain a production possibilities frontier for an economy that produces milk and cookies. Determine what happens to this frontier if disease kills half of the economy's cow population?
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