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Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (5). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed. (a) What are possible y-values? O all positive real numbers O all whole numbers greater than 1 O all real numbers greater than 1 O all integers Ⓒall positive whole numbers (b) List five different outcomes and their associated y-values. Outcome Value of y RRS LRRRLS RALLS S RRRS
Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below. 1 3 0.04 0.05 0.09 0.26 0.33 0.15 0.08 p(x) (a) What is P(x = 4)? P(x-4)= (b) What is P(x s4)? P(x4)= (c) What is the probability that the selected student is taking at most five courses? (d) What is the probability that the selected student is taking at least five courses? (e) What is the probability that the selected student is taking more than five courses?
Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. p(y) 0.63 0.21 0.09 0.05 ? (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) p(4) - (b) How would you interpret p(1) = 0.21? O The probability of one randomly chosen carton having broken eggs in it is 0.21. In the long run, the proportion that will have at most one broken egg will equal 0.21. O In the long run, the proportion of cartons that have exactly one broken egg will equal 0.21. The proportion of eggs that will be broken in each carton from this population is 0.21. (c) Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs. P(y s 2) = Interpret this probability. O In the long run, the proportion of cartons that have exactly two broken eggs will equal this probability. The proportion of eggs that will be broken in any two cartons from this population is this probability. The probability of two randomly chosen cartons having broken eggs in them is this probability. In the long run, the proportion that will have at most two broken eggs will equal this probability. (d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. P(y < 2) = Why is this smaller than the probability in part (c)? This probability is less than the probability in part (c) because the event y = 2 is now not included. This probability is not less than the probability in part (c) because the two probabilities are the same for this distribution. This probability is less than the probability in part (c) because the proportion of eggs with any exact number of broken eggs is negligible. O This probability is less than the probability in part (c) because in probability distributions, Plys k) is always greater than P(y <k).
Consider selecting a household at random in the rural area of a country. Define the random variable x to be x = number of individuals living in the selected household Based on information in an article, the probability distribution of x is as given below. x 1 2 3 4 p(x) 0.140 0.174 0.220 0.260 0.156 Calculate the mean value of the random variable x. 10 5 6 7 8 9 0.023 0.017 0.005 0.004 0.001 Mx