quiz7-key - 4(2 pt Determine the value of E X The Poisson...

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Quiz 7. October 27, 2010 Seat # _________ Name: ___ < KEY > ___ Closed book and notes. No calculator. For Questions 1–3, recall the following three statements. A binomial distribution concerns the number of successes in n Bernoulli trials, when p is the probability of success. A hypergeometric distribution concerns the number of successes in n draws from a population of N items, when K items of the population are successes. The binomial pmf is a good approximation to the hypergeometric pmf when N is "large" and p = K / N . 1. (2 pt) T F When n = 1, the approximation is exact. 2. (2 pt) T F When n = N , the approximation is exact. 3. (2 pt) T F The normal distribution (that is, the bell curve) cannot be used to approximate the binomial distribution, because the normal is continuous but the binomial is discrete. For Questions 4 and 5, consider Problem 4–86. The number of stork sightings on a route in South Carolina follows a Poisson process with a mean of 1.3 per year. Let X denote the time until a stork sighting.
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Unformatted text preview: 4. (2 pt) Determine the value of E( X ). ____________________________________________________________ The Poisson rate is λ = 1 / 1.3 stork sightings per year. The random variable X is exponential. Therefore, from Page 12, E( X ) = 1 / λ = 1 / 1.3 years (per stork) ← ____________________________________________________________ 5. (2 pt) Suppose that a bird watching has been watching for 2 years, with no sighting. Determine the conditional expected value until the next sighting. That is, determine the value of E( X | X > 2). ____________________________________________________________ The exponential distribution is memoryless. Therefore, E( X | X > 2) = E( X ) ← ____________________________________________________________ ______________________________________________________________________ Write on the back any concerns about the weekly quizzes or the course in general. IE 230 – Page 1 of 1 – Schmeiser...
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This note was uploaded on 04/25/2011 for the course IE 230 taught by Professor Xangi during the Fall '08 term at Purdue.

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