BIT 1301 BUSS 202 BSD 1203 BISF 1202 BAC 1202 PROBABILITY AND STATISTICS.
UNIVERSITY EXAMINATIONS: 2021/2022 ORDINARY EXAMINATION FOR BACHELOR OF SCIENCE INFORMATION TECHNOLOGY, BSc. APPLIED COMPUTING, BSD, BISF, BBIT BIT 1301/ BUSS 202/ BSD 1203/ BISF 1202/ BAC 1202: PROBABILITY AND STATISTICS (EVENING/ DISTANCE LEARNING) DATE: DECEMBER, 2021 TIME: 2 HOURS INSTRUCTIONS: Answer Question One and any Other Two Questions QUESTION ONE (a)The arithmetic mean of a distribution is 5.The second and the third moments of the distribution about the mean are 20 and 140 respective. Find the third moment of the distribution about10 [8Marks] (b)A certain distribution has karl pearsons coefficient of skewness 0 ⋅ 4, standard deviation 10 and mean 40.5.Find the mode and the median of the distribution . [8Marks] (c)If 𝐴,𝐵 and 𝐶 are mutually independent events ,show that 𝐴 and 𝐴 ∪ 𝐵 ∪ 𝐶 are independent. [4Marks] QUESTION TWO QUESTION THREE (a) A fair coin is tossed 8 times. (i)What is the probability that the eighth toss results in a head given that preceeding 7 tosses were heads? [5Marks] (ii) What is the probability of getting eight heads or eight tails if the fair coin is tossed 8 times? [5Marks] (b)A student is taking multiple choice exam in which each question has four possible answers ,exactly one which is correct.If the student knows the answer he(she)selects one answer at random from the four possible answers.Suppose that the student knows the answers to 55% of the questions. (i)What is the probability that on a given question the student gets the correct answer? [2Marks] (ii)If the student gets the correct answer to a question what is the probability that he or she knows the answer? [3Marks] QUESTION FOUR (a)Determine the constant 𝑐 so that the function given below is a probability distribution of the random variable 𝑋 . [4Marks] (c)Bank tellers in a certain bank make errors in entering figures in their ledgers at a rate of 0.8 errors per page of entry..What is the probability that in five pages there will be three or more or errors? [3Marks] (d)Use the normal approximation to the binomial to calculate the probability of getting more than 39 defectives in a random sample of 400 taken from a population which is 8% defective. [4Marks]
BIT 1301 BUSS 202 BSD 1203 BISF 1202 BAC 1202 PROBABILITY AND STATISTICS. Read Post »