Let X be uniformly distributed on the interval (0, 1), and let the
conditional distribution of Y given X = x be uniformly distributed on
the interval (−x, x) . (20%)
(a) Find the joint density of (X,Y ) .
(b) Find the conditional density of X given Y = y .
In a sample of size 3 we observe 4, 6 and 8. Can we reject the hypothesis
that μ = 3 against μ ≠ 3 with these data? Use α = 0.05 . (20%)
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