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(a) Let Y = X2 + Z, where Z is a zero-mean unit variance Gaussian rv. Show that no unbiased estimate of X exists from observation of Y. Hint. Consider any x > 0 and compare with -x.
(b) Let Y = X + Z, where Z is uniform over (-1, 1) and X is a parameter lying in (-1, 1). Show that xˆ(y) = y is an unbiased estimate of x. Find a biased estimate xˆ1(y) for which |xˆ1(y) - x| ≤ |xˆ(y) - x| for all x and y with strict inequality with positive probability for all x ∈ (-1, 1).
What are the critical values for z on a one-tailed test if alpha = .01? .001? What would the critical values be at both levels of significance if it was a two-tailed test?
During nine days in a festival, the highest sale of a shop was on sunday and was 900„5 more than the average sale for other days. If the standard deviation of the sale during the festival is 33.33, find the standard deviation leaving that the highes..
State the hypotheses. State the decision rule & sketch it. Find the sample proportions & z test statistic.
Consider the many possible distributions of grades on a quiz in a statistics class; imagine that the grades could range from 0 to 100.
State which of the three diet colas (marked as A, B or C) he or she prefers. Draw a tree diagram depicting the sample space outcomes for the test results.
a small firm has 24 accounts payable of which 14 of the accounts have errors in them. if 7 accounts are chosen at
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.
if the population mean is assumed to be 20 and the sample standard deviation is 5 a score of 15 would have a z-value of
A recent study yielded a positive correlation between breast-fed babies and scores on a vocabulary test taken at age 6. Discuss the potential difficulties in interpreting the results of this study.
question heights of women have a bell-shaped distribution with a mean of 163cm and a standard deviation of 5cm.
a professional employee in a large corporation receives an average of m 42.4 e-mails per day. most of these e-mails
Process of algebraic division and then solving a quadratic equation, find the complex roots. Write down all the factors of the 4th degree polynomial
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