Question: 15. Let X be a continuous random variable with density function f . A number t is said to be the median of X if

15. Let X be a continuous random variable with density function f . A number t is said to be the median of X if P (X ≤ t) = P (X ≥ t) = 1 2 .

By Exercise 7, Section 6.1, X is symmetric about α if and only if for all x we have f (α − x) = f (α + x). Show that if X is symmetric about α, then E(X) = Median(X) = α.

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Problem Overview We are given that X is a continuous random variable with a probability density function f and t is a median of X if PX leq t PX geq t ... View full answer

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