triangular numbers: the first six triangular numbers (1,3,6,10,15,21) are printed one each on one side of a card. the cards are placed face down and mixed. Ch

Question

triangular numbers:
the first six triangular numbers (1,3,6,10,15,21) are printed one each on one side of a card. the cards are placed face down and mixed. Choose two cards at random, and let x be the sum of the two numbers. Construct the probability distribution for this random variable x.

Answer 1

All pairs are equally likely to be drawn (with probability 1/15). So, it's a uniform distribution of all possible pairs:

 

1 + 3 = 4

1 + 6 = 7

1 + 10 = 11

1 + 15 = 16

1 + 21 = 22

3 + 6 = 9

3 + 10 = 13

3 + 15 = 18

3 + 21 = 24

6 + 10 = 16

6 + 15 = 21

6 + 21 = 27

10 + 15 = 25

10 + 21 = 31

15 + 21 = 36