Based on the result of Exercise 8.24, show that if X is a random variable having a chi– square distribution with v degrees of freedom and v is large, the distribution of X – v / √2v can be approximated with the standard normal distribution.
Answer to relevant QuestionsUse the method of Exercise 8.25 to find the approximate value of the probability that a random variable having a chi-square distribution with v = 50 will take on a value greater than 68.0. Use Stirling’s formula of Exercise 1.6 on page 16 to show that when v → ∞, the t distribution approaches the standard normal distribution. Use the result of Exercise 8.41 to show that If the first n1 random variables of Exercise 8.2 have Bernoulli distributions with the parameter θ1 and the other n2 random variables have Bernoulli distributions with the parameter θ2, show that, in the notation of ...There are many problems, particularly in industrial applications, in which we are interested in the proportion of a population that lies between certain limits. Such limits are called tolerance limits. The following steps ...
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