November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
Content preview from Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
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4.2 RANDOM VARIABLE APPROXIMATIONS
The approximations described in this section are not special cases of a random variable for specific finite values of the pdf parameters, but are limiting cases when one or more of the parameters becomes very large. Table 4.1 summarizes some related discrete random variables that are discussed first.
FIGURE 4.1 Modifying a random variable. (a) Conditioning on a related random variable X for a specific value x to give fY|X(y|x). (b) Transforming to a new random variable X with pdf fX(x).
TABLE 4.1 Asymptotic Approximations of Random Variables
| Distribution | Conditions | Approximation |
| Hypergeometric {N, M, n} |  , M/N = p
|
Binomial {n, p} |
| Binomial {n, p} |  ,  , 
|
Poisson 
|
| Negative binomial {m, p} | 
|
Poisson {m(1−p)} |
| Binomial {n, p} | N large | Gaussian ... |
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