part 1 of 3The cdf of the Pareto distribution is0F(x) = 1- - (+)".x+0x > 0.Suppose that a = 2 and 0 = 200. Let X be arandom variable with this Pareto distribution.Find the expectation of X.part 2 of 3Find the median of this Pareto distribution.part 3 of 3Find the mode of this Pareto distribution.

Given the cdf of Pareto distribution of kind II (i.e. Lomax distribution).

Answered: part 1 of 3 The cdf of the Pareto…

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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show step by step The bacterium tropical have diameters that are normally distributed with mean 9 nm and standard deivation 3.8 nm. A researcher does not know these parameters and measures a tropical to have a diameter of 11 nm. What is the probability a randomly-chosen bacterium of this species has a diameter of under 11 nm? To learn what the parameters are for this disease, the researcher measures the diameter of 25 bacteria. What is the probability that a sample of 25 bacteria will have a mean average diameter under 11 nm?
In a human genome there are 6.4X109 basepairs and the mutation rate per generation per basepair is 1.8X10-8 basepairs. What is the expected number of new mutations (not carried by either of your parents) present in you? What is the probability that you contain 20 new mutations? Use Poisson distribution to solve.
Two components are being considered for use in building a system in your manufacturing plant. The lifetime of component 1 is modeled by a normal random variable with mean 20,000 hours and standard deviation of 5000 hours (ignore the fact the this model can technically give negative values for lifetime - that probability is practically zero). The lifetime of component 2 is also a normal random variable but with mean 22,000 hours and standard deviation 1000 hours. Which component has the highest probability of functioning for the life of the system if the target lifetime is 20,000 hours? What about a target lifetime of 24,000 hours?
the environmental protection agency (EPA) limits the amount of vinyl chloride in the plant air emission to no more than 10 parts per millions. suppose a mean emission of vinyl chloride for a partiular plant is 4 parts per million. assume the number of parts per million of vinyl chloride in air sample x follows a Poisson probability distribution what is the standard deviation of the plant is it likely that a sample of air from the plant would yield a value of x that would exceed the EPA limit? explain. note that P(x <=9)= 0.991868
The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5-minute period, Find the expected value and standard deviation. What is the probability that 2 customers will arrive in a 5-minute period? What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?
The expected life of a certain component in a mechanism is treated as a random variable having a gamma distribution with a = 3 and ß = 2. The average expected life of such component is 12 months, what is the probability that this component can have a greater than average expected life?
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