Patrick is doing a card trick using a standard 52-card deck with four suits: hearts, diamonds, spades, and clubs. he shows his friend a card, replaces it, and then shows his friend another card. give the probability that the first card is not a club and the second card is not a heart.

The discrete random variables x and y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 tabulate the distribution and show that a = 0.1.2 find the marginal distributions of x and y. 3 calculate cov(x,y).4 state, giving a reason, whether x and y are independent. 5 calculate e(y|x = 1).