You seem to be calculating the probabilities of X1, X2, and X3. One of them is greater than 1, and the other two are negative.
remember that 0<p<1
A breakdown of the 678 civil cases that were originally tried in front of a judge (rather than a jury) and appealed by either the plaintiff or defendant is repro- duced in the next table. Suppose each civil case is awarded points (positive or negative) based on the out- come of the appeal for the purpose of evaluating federal judges. If the appeal is affirmed or dismissed, +5 points are awarded. If the appeal of a plaintiff trial win is re- versed, -1 point is awarded. If the appeal of a defendant trial win is reversed, -3 points are awarded. Suppose one of the 678 cases is selected at random and the number, x, of points awarded is determined. Find and graph the probability distribution for x.
Am I right/wrong? Suggestions?
With the information im given I assume that each has a probability to happen 1/3. Unless the question is implying that with the greater number of points awarded/subtracted it signifies higher/lower probability.
With my assumption:
P(X1) = 1130/ 2034 = 5/9
P(X2) = 226 / 2034 = 1/9
P(X3) = 678 / 2034 = 3/9 = 1/3
and thus graphed accordingly