Consider throwing 2 usual dice. In each play, we observe the number of dots that stay on top, sum the returned result and to that sum, we apply the rule of casting out nines. For example, if one dice has 6 dots and the other 4 dots, we get a sum of 10 dots, and, casting out nines, we achieve a result of 1.
a) Identify the space of results and the underlined X random variable;
b) How many ways we have to obtain a result of 2, according to the procedure described above?
c) Calculate the value of P(X = 2) and P(X <= 5 | X >= 2) [P -> probability]
d) Calculate the probability function and the probability distribution of X.