The following is a sufficient condition, the Laplace-Liapounoff condition, for the central limit theorem: If X1, X2, X3, . . . is a sequence of independent random variables, each having an absolute third moment
Where Yn = X1 + X2 + · · · + Xn, then the distribution of the standardized mean of the Xi approaches the standard normal distribution when n → ∞. Use this condition to show that the central limit theorem holds for the sequence of random variables of Exercise 8.7.
Answer to relevant QuestionsUse the result of Exercise 8.56 to find the probability that the range of a random sample of size n = 5 from the given uniform population will be at least 0.75. With reference to Example 9.1, what decision would minimize the manufacturer’s expected loss if he felt that (a) The odds for a recession are 3 to 2; (b) The odds for a recession are 7 to 4? Example 9.1 A manufacturer of ...With reference to the definition of Exercise 9.16, find the decisions that will minimize the maximum opportunity loss of (a) Ms. Cooper of Exercise 9.12; (b) The truck driver of Exercise 9.13. With reference to Exercise 9.12, what randomized strategy will minimize Ms. Cooper’s maximum expected cost? In exercise Ms. Cooper is planning to attend a convention in Honolulu, and she must send in her room reservation ...With reference to Example 9.10, for what values of Cw and Cd will Strategy 2 be preferred? Example 9.10 Suppose a manufacturer incurs warranty costs of Cw for every defective unit shipped and it costs Cd to detail an entire ...
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