The probability integral transform

XX is a continuous random variable with (strictly increasing) CDF FF. What is P(F(X)≤0.3)P\big(F(X)\le 0.3\big)? (to 3 decimals)

Show hints (2)+
  1. Rewrite P(F(X) ≤ u) using the inverse F⁻¹.
  2. P(X ≤ F⁻¹(u)) = F(F⁻¹(u)) = u.

Answer

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0.3

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