Table 4.2.4 Number of Co-occurring Addictive Substances Used by Patients in Selected Gambling Treatment Programs

Number ofsubstances used	Frequency
0	144
1	342
2	142
3	72
4	39
5	20
6	6
7	9
8	2
9	1

1. A study by Cross et. al. patients who were involved in problem gambling treatment were asked about co-occurring drug and alcohol addictions. Let the discrete random variable X represent the number of co-occurring addictive substances used by the subjects. Table 4.2.4 summarizes the frequency distribution for this random variable. (a) Construct a table of the relative frequency and the cumulative frequency for this discrete distribution.
   (b) Construct a graph of the probability distribution and a graph representing the cumulative probability distribution for these data.
2. (a) What is the probability that an individual selected at random used five addictive substances?
   (b) What is the probability that an individual selected at random used fewer than three addictive substances? (c) What is the probability that an individual selected at random used more that six addictive substances? (d) What is the probability that an individual selected at random used between two and five addictive substances, inclusive?
   3. Find the mean, variance and standard deviation of this frequency distribution.