Question

This question uses a discrete probability distribution known as the Poisson distribution. A discrete random variable X follows a Poisson distribution with parameter λ if Pr(X = k) = Ake-A ke(0, 1,2, ) k! You are a warrior in Peter Jackson's The Hobbit: Battle of the Five Armies. Because Peter decided to make his battle scenes as legendary as possible, he's decided that the number of orcs that will die with one swing of your sword is Poisson distributed (lid) with parameter λ You swing your sword eight times in the scene. ater, you go see the movie in theaters and record the number of orcs slain during each swing of your sword Sword Swing1 2 3 45 67 8 Orcs Slain 6 4 2 75 1 2 5 Let G (G1,. Gn) be a random vector where Gi is the number of orcs slain on swing i: 1, (6 points) Give the log-likelihood function of G given λ. 2. (8 points) Compute the MLE for λ in the general case. 3, (6 point) Compute the MLE for λ using the observed .

Answer 1

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