Q:I need help with question 12, the picture attached, please!

12. Suppose ( * 1. ..., In ) is a random vector as in the above exercise having a Dirichlet* distribution with parameter vector ( al . ... . ant I ) . Then , let us define new random variables / 1 . ... . In as follows :" * * Y1 = ] _ X 1 - ... _ In` In ... . In = ] _ X1 - ... _ In ( a) Derive the joint density function of ( [ ] . ... . In ) . This is what is called the Dirichlet density of the second kind ; ( b ) Find the marginal density function of Y; for i = 1 , .... n.; Both of topped ( C ) Derive explicit expressions for the mean vector and variance- covariance matrix of ( 1/ 1 . ... , In )