Question: (a) If a random variable X has a Poisson distribution with mean 5, then calculate the expectation E[(2X -3)?] [5 pts] (b) Suppose that X

(a) If a random variable X has a Poisson distribution with mean 5, then calculate the expectation E[(2X -3)?] [5 pts] (b) Suppose that X and Y have joint pdf given by [5 pts] fxy (z,y) = 20 2, 05151,720 otherwise What are the marginal probability density functions for X and Y? (c) A person decides to toss a biased coin with P(heads) = 0.3 repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. Find the variance of Y. [5 pts]

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