Prove that the Poisson probabilities p 0 , p 1 , ........ can be computed recursively by p 0 = e − λ and p k = λ k P k − 1 , k = 1 , 2 , ......... . Find the value of P ( X ≤ 4 ) for λ = 4.5 . Give the comparison of P ( X ≤ 4 ) for λ = 4.5 and the result obtained in problem 28.

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Answer 1

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Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

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Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)…

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Answer 2

Question

Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

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Answer 3

Question

Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

Expert Solution & Answer

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Answer 4

Question

Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

Answer 6

Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

Answer 7

Chapter 2.5, Problem 29P

To determine

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P

Prove that the Poisson probabilities p 0 , p 1 , ........ can be computed recursively by p 0 = e − λ and p k = λ k P k − 1 , k = 1 , 2 , ......... . Find the value of P ( X ≤ 4 ) for λ = 4.5 . Give the comparison of P ( X ≤ 4 ) for λ = 4.5 and the result obtained in problem 28.

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Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

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Chapter 2 Solutions

Prove that the Poisson probabilities p 0 , p 1 , ........ can be computed recursively by p 0 = e − λ and p k = λ k P k − 1 , k = 1 , 2 , ......... . Find the value of P ( X ≤ 4 ) for λ = 4.5 . Give the comparison of P ( X ≤ 4 ) for λ = 4.5 and the result obtained in problem 28.

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Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,.......... Find the value of P(X≤4) for λ=4.5. Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.

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Chapter 2 Solutions

Prove that the Poisson probabilities p0,p1,........ can be computed recursively by p0=e−λ and pk=λkPk−1,k=1,2,..........

Find the value of P(X≤4) for λ=4.5.

Give the comparison of P(X≤4) for λ=4.5 and the result obtained in problem 28.