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Let Q run through the collection of all laws for which EQ f 2 ∞. For the U -statistic Un , show that (a) Un is the unique unbiased estimator T of g(Q) which is symmetric in X1,..., Xn, n ≥ m. Hint: If V = T - Un, EQ V = 0. If Q{xi } = pi , i = 1,..., r, EQ V is a symmetric polynomial S( p1,..., pr ), homogeneous of degree n and 0 for pi ≥ 0 (the restriction J,i pi = 1 can be removed). Show by induction on r that S ≡ 0, then that V ≡ 0. (b) Un is the unbiased estimator of g(Q) with smallest variance. Hint: For an unbiased estimator T with symmetrization W, W = Un by part (a).
Speaking to a group of analysts in January 2006, a brokerage firm executive claimed that at least 70% of investors are currently confident of meeting their investment objectives.
What would be the minimum sample needed to estimate the population mean of the length of carrots using Gro-Haut to within 1.5 cm with 99% confidence?
What is the shape of the theoretical sampling distribution of the mean for samples of (a) 10 if the parent population is normal? (b) 50 if the parent population is not normal?
An experiment consists of drawing four objects from a container, which holds eight operable, six defective, and 10 semioperable objects. Let X be the number of operable objects drawn and Y the number of defective objects drawn.
The standard deviation is 0.73. Would it be unusual to randomly select 10 people and find that greater than 8 recognize the Famous Brand?
Corporation has 2000 male and 500 female engineers. Stratified random sample of 200 male and 50 female engineers provides each engineer. How is the stratified sample different from the SRS?
If a member of the sales force submits an entertainment expense (dinner cost for four) of $190, should this expense be considered unusually high (and possibly worthy of investigation by the company)?
What is the probability that only the first child will have cystic fibrosis? What is the probability that they will have 2 normal sons and 1 daughter with cystic fibrosis?
The level of satisfaction in a consumer survey would represent what level of measurement?
1.Find a peer-reviewed article that provides an example of a study where the researchers utilized linear regression. Briefly describe the study and discuss its findings in your own words.
you toss a fair coin repeatedly until some event happens.a what is the expected number of tosses until the pattern ht
Types of digital cameras are equal, is there evidence of a difference in the mean battery life between the two types of digital cameras at the 95% confidence level?
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