Two children play a game where one child randomly selects three toys without replacement, from a box containing eleven action figures (5 batman, 3 spiderman, 3 wonder woman). She gives away one piece of candy every time she selects a batman, and gets one piece of candy every time she selects a wonder woman. Define X as the total pieces of candy she earns (where earns = wins/loses). S = event that she chooses a spiderman B = event that she chooses a batman W = event that she chooses a wonder woman a) What is the sample space of X? b) What is the PMF of X? c) Show that your PMF is a valid PMF.

The avenues in a particular city run north to south and are numbered consecutively with 1st avenue at the western border of the city. the streets in the city run east to west and are numbered consecutively with 1st street at the southern border of the city. for a festival, the city is not allowing cars to park in a rectangular region bordered by 5th avenue to the west. 9th avenue to the east, 4th street to the south, and 6th street to the north. if x is the avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park? 5th ave 9th ave