Probability and Statistics — DU B.A. (Prog) Mathematics as Major Previous Year Question Papers

DSC -Probability and Statistics Bachelor of Arts / Bachelor of Science a?rogramme) with Mathematics as non-major/minor 1. (a) Construct a stem ahd leafdisplay of the following data: Also, co.mment on interesting. features of the display. (b) Consider the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes: (c) (i) Determine the value of the samplg- standard deviation for each sample, interpret these values and then contrast variability in ,the`two samples. / (ii) Compute the fourth spread for each sample and compare. Zinfandel is a popular red wine varietal produced almost excl.usively in California. It is rather controversi`al among wine connoisseurs because its alcohol content varies quietly substantially from one producer to other. In May 2.003, the author went to the website klwines.Com, randomly selected 10 zinfandels from among the` 325 available, and obtained the. .following values of alcohol content (%) : Calculate mean, median and sample variance. (ii) Sho.w that V(X) = p(1 -p). (iii) Compute E(X79). (b) A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel,10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries. (i) If 6 bottles of wines are to be randomly selected from the 30 for serving, how many ways are there to do this. (ii) If 6 bottles are randomly selected, what is the probability that all of them are the same variiety. (c) For any three events A, 8 and C prove that 3. (a) Six boxes of components arei ready to be shipped by a certain supplier; The number of defective components in each box is as follows `: One of these boxes is to be randomly selected for shipment to a particular customer. Let X be the number of defectives in the selected box. Find pmf (b) Let X be the number of students who show up for a Professor's office hour on, a particular day. Suppose that the pmf of X is p(0) =.20, p(1) .= .25, p(2') = .30, p(3) = .15, and p(4) = .,10. (i) Draw the corresponding pr,obability histogram. (ii) What is the probability that at least two students show up? More than two. students show up? (iii). What is the probability that between .one and three students, inclusive, (iv) What .is the probability that the.professor show.s up? (c) A certain brand of upright freezer is availablei in three different rated capacities: 16 ft3,18 ft3 , and 20 ft3. Let X = the rated capacity of a freezer iof t`his brand sold at a certain s,tore. ,Suppose, that X has pmf k 16 18 20 (i) Compute E(X), E(X2)., and V(X)': (ii) If the price of a freezer having Capacity X is 70X -650, what is the expected price plaid by the next customer to buy ,a freezer? (iii) What is t.he varian`ce of the price paid by the next'icustomer? 4. (a) (b) (c) Each of.six randolnly selecte.d cola drinkers is given a glass containing cola