Solve the following Statistical Problems using R Studio:

a) Consider the following six observations of two variables: X1: 23, 40, 33, 13 X2: 1, 5, 67, 18. Find mean vector for this data set.*

b) Consider the following six observations of two variables: X1: 23, 40, 33, 13. X2: 1, 5, 67, 8. Find covariance for this data set.*

c) Consider the following six observations of two variables: X1: 23, 40, 33, 13. X2: 1, 5, 67, 8. Write down the valuue of Hotelling T Square for testing Ho: mu=[35, 20].*

d) Consider the following six observations of two variables: X1: 23, 40, 33, 13. X2: 1, 5, 67, 8. Find the Statistical sample distance.*

e) Consider the following six observations of two variables: X1: 23, 40, 33, 13. X2: 1, 5, 67, 8. What is the largest eigenvalue obtained from the sample variance and covariance matrix of this data set.*

Solve the following Statistical problems by providing necessary details:

a) Hotelling T square and univariate t square are closely related to the F-distribution.Explain.

b) What are variances obtained from a covariance matrix based on standardized variable?*

c) How many dependent variables are there in a multivariate simple linear regression model?*

d) Units of measurements can be different in Euclidean distances?*

e) What is the distribution of T square for n=20 and p=4?*