Question 1 (14 Marks): using R software

The multivariate observed data is stored in the data file Assignement2.RData. This data frame contains 34 observations of an unknown random bivariate vector X = (X1,X2) with unknown population mean = (1,2) and unknown covariance matrix .

In your answers to (a) - (e) include the R script accordingly.

(a) (4 Marks) Provide the histograms and the appropriate Q-Q plots for testing normality of marginal distributions of X. Give your interpreta- tion.

(b) (2 Marks) Compute the generalized distance for each observation.

(c) (2 Marks) Provide the appropriate Q-Q plot for the distance data ob-

tained in (b). Does X follow a bivariate normal distribution? Explain.

(d) (3 Marks) Provide the 95% confidence ellipse for the population mean

vector = (1, 2).

(e) (3 Marks) Obtain 90% Bonferroni simultaneous confidence intervals for

1 and 2.