I tried to find the estimation through the two cases, but I'm struggling to approach the questions using the maximum likelihood estimation. Thank you!

Use the following for questions 1 and 2. Let X represent the error in making a measurement of a physical characteristic or property (e.g., the boiling point of a particular liquid). It is often reasonable to assume that E(X) = 0 and that X has a normal distribution. Thus the PDF of any particular measurement error is f(x10) = _Le-x420 -00