Suppose J’s team has just entered a tournament in which it will continue to play games until it loses. Let ? denote the total number of goals scored by J in the tournament. Also, let ? be the number of games her team plays in the tournament. a. Find ?[X] b. Find P(X=0) c. Find ?(N=3|X=5).
The number of goals that J scores in soccer games that her team wins is Poisson distributed with mean 2, while the number she scores in games that her team loses is Poisson distributed with mean 1. Assume that, independent of earlier results, J’s team wins each new game it plays with probability ?.
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Find the expected number of goals that J scores in her team’s next game.
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Find the probability that ? scores 6 goals in her next 4 games.
Hint: Would it be useful to know how many of those games were won by J’s team.
Suppose J’s team has just entered a tournament in which it will continue to play games until it loses. Let ? denote the total number of goals scored by J in the tournament. Also, let ? be the number of games her team plays in the tournament.
a. Find ?[X]
b. Find P(X=0)
c. Find ?(N=3|X=5).
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