Simulation and modeling - Old Questions
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9. When is estimation method appropriate? Explain.
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Estimation method estimates the range for the random variable so that the desired output can be achieved. A random variable is drawn from an infinite population that has a stationary probability distribution with a finite mean, μ, and finite variance, σ ². These random variables are independently and identically distributed (i.e. IID variables).
Let xi (i=1,2,…,n) be the n IID random variables. Then normal variate:
In terms of sample mean 
Where, 
Since the sample mean is some of the random variables, it is itself a random variable. So, a confidence interval about its computed value needs to be established. Suppose the model is the normally distributed with mean , Variance σ² and we have a sample of n size then the confidence interval is given by:
, Variance σ² and we have a sample of n size then the confidence interval is given by:
The population variance σ ² is usually not known; in which case it is replaced by an estimate calculated from the formula
In terms of the estimated variance s2, the confidence interval for is defined by
is defined by
Hence the estimation method gives the desired range of the sample variable taken from infinite population.