Obtain sufficient estimators of theta based on a random sanple of size n drawn from the pdf f(x, theta) = e-(x-theta) ; for x>=theta and theta >0 = 0 ; otherwise Use Neyman factorization. Thank you
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Obtain sufficient estimators of theta based on a random sanple of size n drawn from the
f(x, theta) = e-(x-theta) ; for x>=theta and theta >0
= 0 ; otherwise
Use Neyman factorization. Thank you
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- A student attempted to use L’Hopital’s Rule as follows. Did the student make an error, if any, or does it state “no error”?The probability that the Air Conditioning of a brand new car is defective is 10%. Let X be the number of cars with defective AC in a sample of size 100. (a). Find P(X < 6) exactly. (b). ) Find P(X < 6) approximately, using a Poisson approximation (c). Find P(X < 6) approximately, using a normal approximation. Note: For parts (a) and (b), you only need to provide a formal expression each. For part (c), you need to compute the numerical values using the Q-function table (Table 4.2) from the textbook.Let X1,...,Xn be a sample from normal with mean theta and variance 1. Construct an unbiased estimator of theta^2 based from X^2. Find its variance and compare it with the Cramer-Rao lower bound.
- Calculate each of the requested quantities. All of these problems are carefully chosen so that they can be completed without integration, so we are expecting exact answers. For the Gaussian problems, you will sometimes need to lookup values for the standard normal CDF Φ(z).Find kurtosis by using quartile deviation(formula given in picture).By Fermat’s Theorem
- Please explain in the problem below how a) λ was obtained and b) what went wrong with the Poisson approximation. Thank youA single observation of a random variable having a hypergeometric distribution with N = 7 and n = 2 is used to test the null hypothesis k = 2 against the alternative hypothesis k = 4. If the null hypothesis is rejected if and only if the value of the random variable is 2, find the power of the test.Design a 3rd order Least-squares function approximation to interpolate between the mid between (2n and 3") for a dataset as chosen by you. Compute the LS model error.
