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11ProbHw6

11ProbHw6 - IEOR 3658 Probability Prof Mariana...

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IEOR 3658 Assignment #6 Probability October 19, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #6 – due October 26th, 2011 1. A Cure for the Common Cold. The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter λ = 5. Suppose a new wonder drug (based on large quantities of vitamin C) that has just been marketed reduces the Poisson parameter to λ = 3 for 75 percent of the population. For the other 25 percent of the population, the drug has no effect on colds. If an individual tries the drug for a year and has 2 colds in that time, what is the probability that the drug is beneficial to that individual? 2. John has a can of seeds with no label. He is sure that they are either of plant type A or of type B, not both. John has assigned a probability of P ( A ) = P ( B ) = 0 . 5, where A is the event that the seeds are of type A and B the event that the seeds are of type B. We know that each plant grown from seeds A will have white flowers with probability 0.25, while plants

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11ProbHw6 - IEOR 3658 Probability Prof Mariana...

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