. An urn contains 10 balls numbered 1 to 10. Two balls are sampled in turn without
replacement and their numbers are denoted as X1 and X2 respectively. Let Y be the minimum of
X1 and X2.
(a) Show that the distributions of X1 and X2 coincide.
(b) Find expectation and variance of X1.
(c) Find covariance of X1 and X2. Can you guess the sign before calculations? Are X1 and X2 independent
(d) Find expectation and variance of Y .
(e) Find the conditional distribution of X1 given that Y = y.
Hint: the case X1 = y is special
(f) Find expectation and variance of X1 given that Y =