The Poisson mass function is often used in biology to model the number of bacteria in a solution. Suppose a dilute suspension of bacteria is divided into several different test tubes. The number of bacteria \( x \) in a test tube has a Poisson mass function with a parameter \( \lambda \) that represents the mean number of bacterial cells contained in the different test tubes.Express the probability that a particular test tube contains no bacteria, in terms of \( \lambda \).

The probability mass function (PMF) of a Poisson distribution for a random variable X with parameter…

Answered: The Poisson mass function is often used…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The number of cracks that need repair in a section of interstate highway follows a Poisson distribution with a mean of two cracks per mile. Determine the probability mass function f(x) of the number of cracks (X) in 5 miles of highway. Find the probability that there are at least five cracks in 5 miles of highway that require repair. Calculate the mean and variance of X.
The table summarizes results from 981 pedestrian deaths that were caused by automobile accidents. Pedestrian Deaths DriverIntoxicated? Pedestrian Intoxicated? Yes No Yes 44 74 No 277 586 If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated. Please enter a decimal to 4 decimal places.Probability =
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Use normal approximation to estimate the probability of getting exactly 52 girls in 100 births. Assume that boys and girls are equally likely.
A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by Please show complete solution.
An elevator has a placard stating that the maximum capacity is 1344lb long dash—8 passengers. So, 8 adult male passengers can have a mean weight of up to 1344 divided by 8 equals 168 pounds.1344/8=168 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 168lb. (Assume that weights of males are normally distributed with a mean of 171 lb and a standard deviation of 27 lb) Does this elevator appear to be safe? The probability the elevator is overloaded is____
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
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