Robert Vincent Hogg, Joseph Walter McKean, Allen Thornton Craig. Introduction to Mathematical Statistics, 8th edition (Pearson, 2018)

Chapter 3. Some Special Distributions 제3장. 몇몇 특수한 분포

Section 4. The Normal Distributions 제4절. 정규분포

예제(Exercise) 21 및 해설(Solution)

Let f(x) and F(x) be the pdf and the cdf, respectively, of a distribution of the continuous type such that f'(x) exists for all x. Let the mean of the truncated distribution that has pdf g(y) = f(y)/F(y), -∞ < y < b, zero elsewhere, be equal to -f(b)/F(b) for all real b. Prove that f(x) is a pdf of a standard normal distribution.


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