Let the density function of a random variable X be given byV (x) Oxª".Suppose X,X., X, be a random sample, taken from above population. Define anestimator WH-log ( X). Here, the new random variable W, follows,Poisson distribution with mean 0Gamma distribution with mean 90a)b)c)Gamma distribution with mean 0“d)Exponential distribution with meanAnswer

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Answered: Let the density function of a random…

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 useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. Determine a) The half life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)
certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264
Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value x, that represents the 80th percentile of the distribution %3D Enter your answer accurate to TWO decimal places.
Let Z be a st andard normal variable. Let mean and standard derviation > 0 be two real numbers. Then, the distribution of the random variableIs X=emean+standard derviation*Z called the Lognorma (mean,standard derviation) distribution. Write a function to generate random variables from this Lognormal distribution using a transformation method and generate a random sample of size n = 1000. Compare the histogram with the lognormal density curve given by dlnorm function in R.
2. Cytomegalovirus (CMV) is a (generally benign) virus that infects one – half of young adults. If a random sample of 10 young adults is taken, find the probability that between 30% and 40% (inclusive) of those sampled will have CMV. Use the normal approximation with the continuity correction.
Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?

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Let the density function of a random variable X be given by V(x) = 0x"", (0