Let x - 8 d 8 - x mean that x - 8 has the same distribution, Basic Statistics

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Let x - 8 d 8 - x mean that x - 8 has the same distribution

Let X - 8 d 8 - X mean that X - 8 has the same distribution as 8 - X; thus X has a symmetric distribution about 8. Say that Y and X are independent random variables and Y has a distribution which is also symmetric about 8. Show that X - Y has a distribution that is symmetric about zero.

Hint: Write X - Y = X - 8 - ( Y - 8) d 8 - X - (8 - Y) = Y - X.

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Basic Statistics: Let x - 8 d 8 - x mean that x - 8 has the same distribution

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Basic Statistics: Let x - 8 d 8 - x mean that x - 8 has the same distribution

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