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

Your Roll Number. All questions within each section are to be answered in a contiguous manner on the answer sheet. Start each question on a new page, and all subparts of a question should follow one after the other. All intermediate calculations should be rounded off to 3 decimal places. The values provided in statistical tables should not be rounded off. All final calculations should be rounded off to two decimal places. Statistical tables are attached for your reference. This paper contains two sections. Attempt both sections. 1. (a) Let Xi, X2, .... Xn be a random sample from a Poisson distribution with parameter 2, whose probability mass function is given by: I. Derive the Maximum Likelihood Estimator (MLE) of 1. Il. If a random sample of size 5 yields the observations 2, 0, 3, 1, 2, compute the MLE of 1 for this sample. (7+3) 2. (a) A study assumes that the weekly time a college student dedicates to playing football platforms (X) follows a distribution with an average of 20 hours and a standard deviation of 4 hours. A random sample of 60 students is chosen. Find the probability that the sample mean of weekly time devoted for football falls between 19.8 and 21.1 hours. (b) Let the random variables X, Y and Z have the mean as 2, -3 and 4 and the variances as 1, 5 and 2, respectively. Moreover, the covariance between X and Y is - 2, between X and Z is - 1 and between Y and Zis 1. Find the mean and variance of W = 3X - Y + 2Z. (5+5) (a) Show that the sample variance s" _ I*-x)? n-1 is an unbiased estimator of the population variance o', i.e., show that E(S<) = o'. (b) Let X1, Xz. ....Xn be a random sample from a population with the following probability density function: Derive the Method of Moments estimator of 0 and hence compute the estimate when a sample of size 4 gives observations: 0.2, 0.5, 0.7, 0.4. (10+5) 4. Let Y be the number of on line orders received per day by a randomly selected e-commerce retailer. The probability mass function of Y is given as follows: (a) Consider a random sample of two retailers, obtain the probability distribution of Ý (sample mean). Consider a random sample of two retailers, obtain the probability distribution of S' (sample variance). (c) Calculate P(S? > 2.5) and P(1.1 < S2 < 6.5), when a random sample of size 2 is selected. (5+5+5) (a) An economist is conducting a household consumption survey to estimate the average monthly expenditure on food incurred by households in an urban locality. A random sample of 16 households is selected. The survey results show that the sample mean monthly food expenditure is 78,400, and the sample standard deviation is 71,200. Assuming that the population is normally distributed and the population standard deviation is unknown, construct a 95 percent confidence interval for the population mean of monthly food expenditure.