申論題

3. (10%) Assume that X is a random variable with a probability density function f(x) that is positive and continuous when a ＜ x ＜ b; zero elsewhere. The distribution function F(x) of X may be written
  
F(x) = 0 when x ≤ a, and F(x) = 1 when x ≥b. Assume that there is a number M of the distribution with F(M)=0.3. Let X₁, X₂ and X₃be a random sample from this distribution. LetY₁＜Y₂ ＜Y₃ denote the order statistics of the sample. Please compute the value of Pr(Y₂ ＜ M).