Question

You roll two dice. Let Y be a random variable that is the larger of the two rolls (or, if the rolls are the same, your random variable is that value).

Write Y as a function from the outcome space to the real number

What is the distribution of Y?

What is P(Y≥5)?

Answer 1

[1][1], [1][2], [1][3], [1][4], [1][5], [1][6],
[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],
[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],
[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],
[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],
[6][1], [6][2], [6][3], [6][4], [6][5], [6][6]

Sample space of Y = {1, 2, 3, 4, 5, 6}

P(Y=1) = 1/36

P(Y=2) = 3/36 = 1/12

P(Y=3) = 5/36

P(Y=4) = 7/36

P(Y=5) = 9/36

P(Y=6) = 11/36

P(Y≥5) = ?

P(Y≥5) = P(Y=5) + P(Y=6)

P(Y≥5) = 9/36 + 11/36

P(Y≥5) = 20/36

P(Y≥5) = 5/9