STAT330 Lecture Notes - Monotonic Function, Uniform Boundedness, Glossary Of Video Game Terms
9 Feb 2014
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Unfortunately, nding the distribution exactly is often very di cult or very time-consuming even if the joint distribution of the random variables is known exactly. In other cases, we may have only partial information about the joint distribution of x1, , xn in which case it is impossible to determine the distribution of y . However, when n is large, it may be possible to obtain approximations to the distribution of y even when only partial information about. X1, , xn is available; in many cases, these approximations can be remarkably accurate. This approach, of course, is very common in mathematics. For example, if n is large compared to x, one might approximate (1 + x/n)n by exp(x) since n (cid:10)1 + lim x n(cid:11)n. = exp(x). (however, this approximation may be very poor if x/n is not close to 0. ) A more interesting example is stirling"s approximation, which is used to approximate n! for large values of n:
