2. Consider the model
$X = aY_1 + Y_2$,
where $Y_1 \sim N(0,2)$ and $Y_2 \sim N(0, \sigma^2)$. The random variables $Y_1$ and $Y_2$ are independent.
Let $(X_1, X_2, ..., X_n)$ be the observed random sample and $(Y_{11}, Y_{12}, ..., Y_{1n})$ be the missing
observations.
a. Derive the EM estimates for $a$ and $\sigma^2$.
(6 marks)
b. Write a R program to obtain the EM estimates for $a$ and $\sigma^2$.
(4 marks)
