Cram R's Theorem

Cram R's Theorem

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical statistics, Cram r's theorem (or Cram r's decomposition theorem) is one of several theorems of Harald Cram r, a Swedish statistician and probabilist. Cram r's theorem is the result that if X and Y are independent real-valued random variables whose sum X + Y is a normal random variable, then both X and Y must be normal as well. By induction, if any finite sum of independent real-valued random variables is normal, then the summands must all be normal. Thus, while the normal distribution is infinitely divisible, it can only be decomposed into normal distributions (if the summands are independent). Contrast with the central limit theorem, which states that the average of independent identically distributed random variables with finite mean and variance is asymptotically normal. Cram r's theorem shows that a finite average is not normal, unless the original variables were normal.show more

Product details

  • Paperback | 92 pages
  • 152 x 229 x 6mm | 145g
  • Fidel
  • United States
  • English
  • 613672782X
  • 9786136727820