Suppose that a fair coin is tossed ten times independently. Let V be the number of tails obtained on the ten tossed. Determine the possible value of V. 1. 2. Let the random variable X denotes the number of automobile accidents per week at a busy intersection in a large city. In a 100-week period, there were no accidents in 50 of the weeks, one accident in 30 of the weeks, two accidents in ten of the weeks, and three accidents in ten of the weeks. Based on this information, define the probability distribution function for the number of accidents per week. 3. Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the outcomes of the sample space S for the three tosses of the coin and to each sample point assign a value w of W. 4. During the summer months, a rental agency keeps track of the number of speedboats rented each day during a period of 90 days. The variable X represents the number of speedboats rented per day. The results are shown as follow. 2 Number of days 45 30 15 (a) Compute the probability P(X) for each X. (b) Construct a probability distribution and graph for the data. 5. Suppose that two balanced dice are rolled, and let Q denote the absolute value of the difference between the two numbers that appear. Determine the probability function of Q. 6. Suppose that a box contains seven red balls and three blue balls. If four balls are selected at random without replacement, determine the probability distribution of the number of red balls that will be obtained. 7. A shipment of seven computer sets contains four defective sets. A company makes a random purchase of three of the sets without replacement. If z is the number of defective sets purchased by the hotel, find the probability distribution of Z. 8. X denotes the number of vacant seats on a passenger flight, and let the probability distribution function be 1 Pr(X=x) 0.50 0.30 0.15 0.05 Suppose the random variable Y denotes the amount of revenue lost due to vacant seats. If each vacant seat costs the airline RM 70 in lost revenue, (a) find the expression of Y in terms of X, (b) find the probability distribution function of Y. 9. Ten percent from members of club A always pay their member fees lately. Three members are selected at random. If X were a number of members that always pay their fees lately, prove that it is a discrete random variable. A box is containing four red marbles and two blue marbles. Three marbles are drawn in succession without replacement from that box. Let discrete variable Y be a number of blue marbles. Show that Y is discrete random variable and find the probability distribution. 10.