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 .

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Given that;

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orchestra answered 1 year ago

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