(a) Find P(X1X2), P(X1X2,X1X3),..........P(X1Xi, i=1,2,3........n)
(b)Suppose the sampling continues until X1 is no longer the smallest observation,(i.e., Xj X1 Xi, i=2,3,.......,j-1). Let Y equal the number of trials until X1 is no longer the smallest observation, (i.e., Y=j-1). Show that the distribution of Y is
P(Y=y)=1/(y(y+1)), y=1,2,3.....
(c) Compute the mean and variance of Y if they exist.
(b)Suppose the sampling continues until X1 is no longer the smallest observation,(i.e., Xj X1 Xi, i=2,3,.......,j-1). Let Y equal the number of trials until X1 is no longer the smallest observation, (i.e., Y=j-1). Show that the distribution of Y is
P(Y=y)=1/(y(y+1)), y=1,2,3.....
(c) Compute the mean and variance of Y if they exist.