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Let T and S be two statistics such that S = ψ(T ) for a measurable ψ. Show that
(a) if T is complete, then S is complete;
(b) if T is complete and sufficient and ψ is one-to-one, then S is complete and sufficient;
(c) the results in (a) and (b) still hold if the completeness is replaced by the bounded completeness.
The scores, X, of an examination may be assumed to be normally distributed with μ = 70 and σ2 = 49. What is the probability that:
1. in a statistical test of hypotheses we reject the null hypothesis at alpha ifa the p-value is smaller than alpha.b
in a sample of 200 surgeons 30 were in favor of government controlled healthcare while in a sample of 150 general
The Delaware Lottery is offering customers a chance to win $10,000. Customers pay $5.00 for a ticket (there are 3000 tickets sold only). Second prize is $1,000. If a customer buys only one ticket, find the expected value of this lottery game.
A person has a chance to invest $50,000 in a business venture. If the venture works, the investor will reap $200,000. If the venture fails, the investor will lose his money. It appears that there is about a .50 probability of the venture working. ..
American youngsters aged 6 to 19, 15% were seriously overweight. Calculate and interpret a confidence interval using a 99% confience level for the proportion of all american youngsters.
If "Some obsessive-compulsive behaviors are not curable diseases" is true, what is the truth value of the following statements?
Suppose that X1,..,Xn form a random sample from the normal distribution with unknown mean M and unknown standard deviation S, and let m and s denote the MLEs of M and S. for the sample size n=17, find a value of k such that P(m > M +ks) = 0.95
The probability that an individual egg in a carton of eggs is cracked is 0.03. You havepicked out a carton of 1 dozen eggs (that’s 12 eggs) at the grocery store.
the number of people arriving for treatment at an emergency room can be modeled by a poisson process with a rate
A researcher wants to determine a 95% confidence interval for the mean number of hours that UMKC students spend doing homework per week.
Your assignment is to write a 5-7 page discussion to: (1) define the canonical correlation statistical procedure, discuss how regression analysis plays a central role in canonical correlation, explain how to interpret the canonical correlation;
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