(a) Let X1, X2, X3, X4 be a sample from U(0, 1), and let X(1), X(2), X(3), X(4) be the cor - responding order statistics. Find the probability density function for each of the random variables: i. X(2) [1] ii. X(3) – X(1) [1] iii. X(4) — X(2) [1] iv. 1 – X(3)

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A: Solution

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A: Step 1: Step 2: Step 3: Step 4:

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A:

Q: Illustrate the null hypothesis for a correlated t test?

A:

Q: Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

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A: Given Data: n1=15 n2=15

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Q: Let X; be independent Uniform(-7,7) random variables, for i=1, 2, ..., 7. Let Y=X₁+X₂+...+X7. (b)…

A: