Suppose ( * 1., In ) is a random vector as in the above exercise having a Dirichlet* distribution with parameter vector ( al . ant I ) . Then , let...

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 randomvariables / 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 Dirichletdensity 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 ) .