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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).
A random sample is selected from a normal population. The population mean is 60 and the standard deviation is 15. after treatment the sample mean is 65. the sample size is 25.
the pulse rates for 13 adult women were as follows. construct a 0.95 confidence interval for the mean pulse rate. give
briefly restate your research area of interesta. identify at least 2 variables for which you would utilize a
a population of cereal boxes has a normal weight with a mean of 16 ounces and a standard deviation of 0.2 ounces. if a
B reports to C's statement to A. If A asserts that B denies that C claims D is a liar, what is the probability that D spoke the truth?
The table below contains the opinions of a sample of 200 people (broken down by gender) about the latest congressional plan to fund abortion clinics.
What score would Sandra need to beat 91 percent of her mathematics class? The mean score was 73, and the standard deviation was 12.
a simple random sample of 40 salaries of ncaa football coaches as a mean of 415953 and a standard deviation of 463364.
the height of woman ages 20-29 is normally distributed with a mean of 64.4 inches. assuming the standard diviation
Are the factors to be considered fixed effects? Does it seem reasonable that if you were to repeat the survey, you would select the same sexes and species?
Find out the least-squares regression line and interpret its slope.
Using z-scores, a population with mean = 37 and standard deviation = 8 is standardized so that the new mean is mean = 50 and standard deviation = 10. How does an individual's z-score in the new distribution compare with his/her z-score in the orig..
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