Define probability definition of continuity

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Probability Definition of Continuity
1. Let a, b be real numbers with a < b. Suppose that f_x is the probability density function (PDF) of a continuous random variable X. Also suppose that f_x is continuous on (a, b), and that, for every subinterval I of (a, b), the probability P(X E I) only depends on the length of I, while f_x(x) = 0 if x -E- [a, b]. Use the definition of continuity to prove that f_x is constant on (a, b). Hint: Try a proof of contradiction. Note: We say that X is uniform on (a, b) if f_x satisfies the conditions given above.

Reference no: EM13118350

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