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August 12th, 2008, 11:08 AM   #1
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Need Help Please!!! Probability ans Stats

An astrophysicist has a theory which suggests that measurements of the temperature of the background
radiation in the universe should all have the same mean ? but that the variance of a measurement made
in the plane of the Milky Way galaxy should be 4 times as large as the variance of a measurement made
in a direction at right angles to the plane of the galaxy. Observations X1, X2, . . ., X15 are available
in the galactic plane, Y1, Y2, . . ., Y10 at right angles to it. All observations are independent.
The random variable T = aX + bY is to be used as an estimator for ?. Find values of a and b such
that the expectation of T is equal to ? and the variance of T is as small as possible.


and


The Football Association invites 12 referees to watch a video of a football match and record how many
yellow cards they would have awarded. The 12 numbers recorded are to be treated as a simple random
sample. The F.A. regards a standard deviation of 1.2 yellow cards as demonstrating an acceptable
level of consistency. The sample standard deviation, though, is 2.2 yellow cards. Are the referees
inconsistent?
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