Question: 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)

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?

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