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Sol_Exam_STD_T110 - TERM 1 STANDARD EXAMINATION 2010...

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TERM 1 STANDARD EXAMINATION 2010 CONCEPTUAL FOUNDATIONS — MATH21001 INSTRUCTIONS SHEET 1. Answer all questions in the Examination Answer Booklet provided. 2. Working and formulae must be shown to gain full marks in any question that requires calculation. 3. Write your name in the Question Paper and Rough Working Paper, and return those with the Examination Answer Booklet. Page 1 of 9
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TERM 1 STANDARD EXAMINATION 2010 CONCEPTUAL FOUNDATIONS — MATH21001 Question 1 (1 mark for each question) 10 Marks State whether each of the following is ‘true’ or ‘false’. (a) The standard deviation of a set of observations can be greater than the range. (Range is the difference between the maximum value and the minimum value.) Answer: False (b) Poisson distribution is a one parameter distribution. That is, if we know the mean, we can find the probability distribution of a Poisson process. Answer: True (c) A normal probability plot will trace a straight line if the data comes from a normal (or Gaussian) distribution. Answer: True (d) In hypothesis testing, we can reduce both Type I and Type II errors at the same time by increasing the sample size. Answer: True (e) If the Durbin-Watson statistic is zero, that indicates there is no autocorrelation in the residuals of the linear regression model. Answer: False (f) In a recursive algorithm, the same problem solving tool is applied repeatedly. Answer: True (g) In Boolean algebra, an OR gate can be replaced by a combination of AND and NOT gates. Answer: True (h) In pseudocode or Java, if we write a += b , it means that we add a with itself repeatedly b times. Answer: False (i) An NP-complete problem indicates a more difficult problem than an NP-hard problem. Answer: True (j) There are five nucleotides in DNA. Answer: False Question 2 6 Marks (a) Suppose that you have contributed to a portfolio of $10,000 invested in a risky venture. The income ( X ) in dollars that will be earned on this portfolio over the next year has the probability distribution given in the table below. Determine the expected value of the income earned on this portfolio next year. Page 2 of 9
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TERM 1 STANDARD EXAMINATION 2010 CONCEPTUAL FOUNDATIONS — MATH21001 Probability Distribution Income in dollars ( X ) P ( X ) 500 0.4 1,000 0.3 2,000 0.2 3,000 0.1 Answer: Expected value of income = 500(.4) + 1000(.3) + 2000(.2) + 3000(.1) = $1200 (3 marks) (b) A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 24 seeds. What is the probability that exactly 20 germinate?
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