Question

The likelihood of two fraudulent dice coming in pairs is six times the likelihood of a single coming. The opposite faces of these dice are painted in for the same color, in three color. Both dice are painted 1 to 6 red, 2 to 5 green and 3 to 4 blue colors. Two dice are being thrown together. The X-rassal variable is 0, if is the same color as the colors on the faces on top. The X-rassal variable is 1, if one is red and the other is blue. The X-rassal variable is 2, if one is red and the other is green. The X-rassal variable is 3, if one is blue and the other is green.

a) Write the probability function f (x) of x as a table (show how each f (x) value is found)

b)Write the cumulative probability function f (x) of x

Answer 1

There can be 36 different possible outcomes on rolling two dice

X = 0 if both the dice has same color for the outcomes

{(1,1), (1,6), (6,1), (6,6), (2,2), (2,5), (5,2), (5,5), (3,3), (3,4), (4,3), (4,4)}

X = 1 for the outcomes {(1,3), (1,4), (6,3), (6,4), (3,1), (4,1), (3,6), (4,6)}

X = 2 for the outcomes {(1,2), (1,5), (6,2), (6,5), (2,1), (5,1), (2,6), (5,6)}

X = 3 for the outcomes {(3,2), (3,5), (4,2), (4,5), (2,3), (5,3), (2,4), (5,4)}

(a) The PMF of X is

X	0	1	2	3
P(X = x)	1/3	2/9	2/9	2/9

(b) The cumulative probability function of X is

F(X = x) = 0, x < 0

F(X = x) = 1/3, 0 ≤ x < 1

F(X = x) = 5/9, 1 ≤ x < 2

F(X = x) = 7/9, 2 ≤ x < 3

F(X = x) = 1, x ≥ 3