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Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$.

  1. $3 (1 - b) a (b - a)$
  2. $3 (b - a) - (b^{2}- a^{2})/2)$
  3. $6 (1 - b) a (b - a)$
  4. $(1 - b) a (b - a)$
  5. $6 ((b^{2}- a^{2})/ 2 - (b^{3} - a^{3})/3)$.
asked in Probability by Veteran (38.7k points)   | 102 views

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