Introductory Statistics for Economics — DU B.A. (Hons.) Economics Previous Year Question Papers

Do any two questions. 1. (a) A test for ovarian cancer has a 5 percent rate of false positives and a O percent rate of false negatives. On average, 1 in every 2,500 women in XYZ country over age 35 actually has ovarian cancer. If a woman over 35 tests positive, what is the probability that she actually has cancer? Explain using a tree diagram. (b) Citibank recorded the number of customers using a downtown ATM during the noon hour on 20 consecutive workdays. (i) Find the sample mean, median, and 10% trimmed mean of the above data. (i) Is the data symmetric or skewed? If skewed, then what is the direction? A parallel system works if at least one of its components is working. Consider a parallel system of n components, where each component works independently with probability 1/2. The system fails only if all of its components fail. What is the probability that component 1 is working, given that the system is functioning? (5) (b) Consider the following frequency distribution : (i) Calculate relative frequency and density for the data. (ii) What proportion of the observations are at least 6? (3+2) 3. (a) A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.96, and the probability that both components do so is 0.75. Given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also? (5) (b) Let a and b be constants, and let y; = ax, + b for i = 1,2, ..., n. What are the relationships between andy and between S* and sy. Provide appropriate proofs for the same. (5) 4. The distribution function of a discrete random variable X is given by x <0 (v) Derive the probability mass function of X. (2x5=10) 5. The probability density function of a continuous random variable X is given by f(x) = jK(1 - x3), -1≤x ≤ 1, otherwise. (i) Find the value of k. (ii) Find the cumulative distribution function of F(x). (iv) Find E(X) and Far(A). SECTION III 6. (a) The marks in a statistics test are normally distributed with mean = 70 and standard deviation = 8. (i) If the top 5% of students receive distinction, what is the minimum score required for distinction? (i) Find the fourth spread of the marks distribution. 1 (b) A shipment contains 500 electronic chips, of which 25 are defective. A quality inspector selects 20 chips for testing without replacement. Let A be the number of defective chips found in the sample. (i) State the exact distribution of A. (i) Find the approximate probability, (X = 2). Which distribution would you use? (iii) Find the expected number of defectives in the sample.