What is the step by step solution for solving the given problem? Searching the Web I am overwhelmed with many formulas and less illustrative examples.
Given a Gaussian distribution with unknown mean $\mu$ and variance=1, we want to estimate $\mu$ with an accuracy of epsilon and confidence interval of ci. What is the minimum number of iid samples we would need?
The number of samples you need depends on your estimator.
For example, the maximum likelihood estimator of the mean of a Gaussian is the sample average: $\frac{1}{n} \sum_{i=1}^n x_i$. Note that the sample average for a sample of $n$ i.i.d. $N(\mu,1)$ random variables follows a $N(\mu,\frac{1}{n})$ distribution.
Using this, you can find the probability that the estimate is in the interval $(\mu-\epsilon, \mu+\epsilon)$ as a function of the number of samples $n$ by using the cumulative distribution function of $N(\mu,\frac{1}{n})$ .