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Two people enter the elevator in a 5-floor building. Let N1 and N2 denote the floors...

Two people enter the elevator in a 5-floor building. Let N1 and N2 denote the floors that they want to go. Assume that ?1 and ?2 are independent and equtl to 2, 3, 4 and 5 with probabilities 1/4 each.

  1. (a) Write down the joint PMF

  2. (b) Calculate ? (?1 > ?2) and ? (?1 = ?2)

  3. (c) Let ?1 and ?2 denote the number of stops that each of them will make before arriving to their floor. What is the support of ?1 and ?2?

  4. (d) Find the marginal PMF-s and the joint PMF of ?1 and ?2. Are they independent?

  5. (e) Calculate ? (?1 = ?2)

  6. (f) Calculate C???(?1, ?2)

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