Answer:
[tex]P_X(1) = 9/19 [/tex]
[tex] P_X(-1) = 10/19 [/tex]
Step-by-step explanation:
You need to take the payment and substract $1 from them, corresponding to the bet cost. With this in mind, you will win $1 with probability 18/38 = 9/19 and you will lose $1 with probability 20/38 = 10/19. With this in mind, the distribution of X is given by the following probability mass function, with range {-1,1}
[tex]P_X(1) = 9/19 [/tex]
[tex] P_X(-1) = 10/19 [/tex]
