Jane chooses a number X at random from the set of numbers
{1, 2, 3, 4}, so that
P(X = k) =
1
4
for k = 1, 2, 3, 4.
She then chooses a number Y at random from the subset of
numbers {X, ...,
4
}; for example, if
X = 3, then Y is chosen at
random from {
3,
4}
.
(i) Find the joint probability distribution of X and Y and display
it in the form of a two-way table.
[5 marks]
(ii) Find the marginal probability distribution of Y , and hence
find E(Y ) and V ar(Y ).
[4 marks]
(iii) Show that Cov(X, Y ) = 5/8.
[4 marks]
(iv) Find the probability distribution of U = X + Y . [7