Probability and Statistics - Maximum Likelihood Estimation and Chi-Square Test

Let X an unknown random variable with unknown mean u and unknown variance a2, and with n = 24 samples: 16.3 20.9 16.9 17.5 18.9 20.4 21.0 21.1 19.7 19.9 17.4 20.6 22.7 21.8 16.6 15.3 18.0 20.1 23.2 20.2 20.3 16.0 17.2 19.7 (a) Write down the formula for the MLE and 32 if X is a normal random variable. (There is no need to show the proof this time, but remember that you might be asked to prove the formula in the nal exam.) Let A1, . . . ,A be the event given by AE. := {17+i221}. Compute the function Q in the chisquare test. (Show your work) (c) Can you reject the hypothesis that X is a normal random variable with significance level a = 0.10? (Show your work)