Suppose that we observe that the Patriots have won 2 games (and the number of ga

Question

Suppose that we observe that the Patriots have won 2 games (and the number of games that have been losses is some unknown number). Suppose the probability of them winning an individual game is 0.6 and that all games are independent.

a. Let n denote the total number of games that the Patriots have played. Clearly state the param. space of n, after observing all of the data.

b. If X is equal to the random variable for the # of games that the Patriots have played. Clearly state the param. space of n, after observing all of the data.

c. Find the MLE for n. Justify your answer (i.e. show using math that the maximum of the likelihood function over the param. space does occur there.) HINT: 1.4/0.6=2.33

d. Write a sentence to explain intuitively what the value of n that you got means

Explanation / Answer

(a) since it is alraedy given that patriots have won 2 games n>=2. Hence the parameter space for n can be n>2

(b) X is a random variable with X>2 as the state space since two games have already been won by patriots

(c) since 2 games = 0.6 then total number of games should be 20/6 should be the average value of n which is the MLE of the n

(d)Intuitively it means that if 20/6 games is played 2 games can be won by the patriots making 0.6 as the winning probability

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