(Solved): HWA2. Consider the "degenerated" statistical linear regression model \( Y=\beta_{0}+\epsilon \), w ...

HWA2. Consider the "degenerated" statistical linear regression model \( Y=\beta_{0}+\epsilon \), where \( \epsilon \) is a normally distributed random variable with mean 0 and variance \( \sigma^{2} \), with \( \sigma \) unknown. Suppse a random sample \( Y_{i} \), \( i=1,2, \ldots, n \) is collected, that is \[ Y_{i}=\beta_{0}+\epsilon_{i} . \] with \( \epsilon_{1}, \epsilon_{2}, \ldots, \epsilon_{n} \) independent and identically distributed as \( \epsilon \). (a) Find the mamximum likelyhood estimation for \( \beta_{0} \). (b) Find the maximum likelyhood estimation for \( \sigma^{2} \).