Let X denote the number of bombs hit per minute in an area of 1 square miles on a certain day during a war. Suppose has a Poisson distribution with λ = 5. a) Find the probability that two bombs hit that area in a minute. b) Find the probability that at most two bombs hit that area in a minute. c) Find the expected number of bomb hits per minute in that area.

Let X denote the number of bombs hit per minute in an area of 1 square miles on a certain day during a war. Suppose has a Poisson distribution with λ = 5. a) Find the probability that two bombs hit that area in a minute. b) Find the probability that at most two bombs hit that area in a minute. c) Find the expected number of bomb hits per minute in that area.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Assume that the height of male students in a large university is normally distributed with mean 172.7 cm and variance 57.76 cm². (a) Suppose 80 random samples, each with 25 male students are obtained. In how many samples would you expect the sample mean to be between 169.66 cm and 173.46 cm? Give you answer to one decimal place. Answer: number of samples = (b) Suppose 6 random samples, each with 25 male students are obtained. Compute the probability that exactly 4 of the 6 samples will have its sample mean between 169.66 cm and 173.46 cm. Give your answer to two decimal places. Answer: probability=
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A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore. A) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. B) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. C) Compute ?, the expected value of the number of fish caught per fisherman in a 6-hour period (round "at least 4" to 4). D) Compute ?, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round "at least 4" to 4).
JUR 1. Suppose the lifetime of a particular brand of light bulbs is exponentially distributed with a mean of 400 hours. a) Find the probability that a randomly selected light bulb would last over 500 hours. b) Find the probability that a randomly selected light bulb would last under 300 hours. lu colected light bulbs would last over 500 67
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5. Suppose that the number of insects caught in a spider's web in one day follows a Poisson distribution with rate = 2.6. For the questions that follow, make sure to define a random variable, state its distribution (including parameters), and translate the question into a probability statement. %3D wg probal b What is the probability that the spider catches at least one insect in 12 hours? PUS 18)
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
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10. Define Beta distribution of first kind. Find its mean and variance. CS Scanned with CamScanner