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A random variable X can take rational values of the types n/(n+1) and (n+1)/n, where n = 1, 2, 3,.... If P(X = n/(n+1)) = P(X = (n+1)/n) = (1/2)^(n+1), then which of the following statements is true?
- P(X < 1) = P(X > 1)
- P(1/2 < X < 1) < P(X > 1)
- P(X > 3/2) < P(X < 1)
- All of the above are true
Correct answer: All of the above are true
Solution
All the statements are true because they reflect the distribution of probabilities for the values of X. The probabilities assigned to each value ensure that the cumulative probabilities for the intervals specified in the statements maintain the relationships described, confirming the validity of each statement.
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