Question

In: Statistics and Probability

Suppose that X1, X2, X3, X4 is a simple random (independent and identically distributed) sample of...

Suppose that X1, X2, X3, X4 is a simple random (independent and identically distributed) sample of size 4 from a normal distribution with an unknown mean μ but a known variance 9. Suppose further that Y1, Y2, Y3, Y4, Y5 is another simple random sample (independent from X1, X2, X3, X4 from a normal distribution with the same mean   μand variance 16. We estimate μ with
U = (bar{X}+bar{Y})/2.

where

bar{X} = (X1 + X2 + X3 + X4)/4

bar{Y} = (Y1 + Y2 + Y3 + Y4+ Y5)/5
a. (6 points) Determine the distribution of U.
b. (4 points) Build a 99% confidence interval for μ.
c. (6 points) Compute the coefficient of correlation between U and X1 .

Solutions

Expert Solution

Given that;

Solution;



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