Suppose that \(Y_{1}, \ldots, Y_{n}\) are i.i.d. random variables with a \(N(1,4)\) distribution. Sketch the probability density of \(\bar{Y}\) when \(n=2\). Repeat this for \(n=10\) and \(n=100\). In words, describe how the densities differ. What is the relationship between your answer and the law of large numbers?