4 A pond has N fish. John caught 100 fish, tagged them, and relea mem back to the pond. He then caught 50 fish, among them 10 are tagged. 1. Give an estimate of the number of fish in the pond; 2. If the pond has 400 fish (N = 400), and X is the number of fish John cau_ in the second time. Write down Sx, the range of X, and the p.m.f. of %3D 3. In the scenario of part 2; first compute the exact P(Y

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Problem 4 A pond has N fish. John caught 100 fish, tagged them, and released
them back to the pond. He then caught 50 fish, among them 10 are tagged.
1. Give an estimate of the number of fish in the pond;
2. If the pond has 400 fish (N = 400), and X is the number of fish John caught
in the second time. Write down Sx, the range of X, and the p.m.f. of X.
%3D
3. In the scenario of part 2; first compute the exact P(X = 10), and then
approximate this probability by a binomial distribution.
%3D
Transcribed Image Text:Problem 4 A pond has N fish. John caught 100 fish, tagged them, and released them back to the pond. He then caught 50 fish, among them 10 are tagged. 1. Give an estimate of the number of fish in the pond; 2. If the pond has 400 fish (N = 400), and X is the number of fish John caught in the second time. Write down Sx, the range of X, and the p.m.f. of X. %3D 3. In the scenario of part 2; first compute the exact P(X = 10), and then approximate this probability by a binomial distribution. %3D
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