DISTRIBUTION 3.1 RANDOM VARIABLES AND PROBABILITY DISTRIBUTION Random variables is a quantity resulting from an experiment that‚ by chance‚ can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable. 3.2 DISCRETE RANDOM VARIABLE A random variable is called a discrete random variable if its set of
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i=1 n i=1 xi = a n x ¯ where x = ¯ 1 n i=1 xi 4. FALSE If X and Y are independent random variables then: E (Y |X) = E (Y ) 1 5. TRUE If {a1 ‚ a2 ‚ . . . ‚ an } are constants and {X1 ‚ X2 ‚ . . . ‚ Xn } are random variables then: n n E i=1 ai X i = i=1 ai E (Xi ) 6. FALSE For a random variable X‚ let µ = E (X). The variance of X can be expressed as: V ar(X) = E X 2 − µ2 7. TRUE For random variables Y and X‚ the variance of Y conditional on X = x is given by: V ar(Y |X = x) = E Y 2 |x
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Simulation can be used as a pedagogical device to reinforce analytic solution methodologies. Nc et ia -2- • By changing simulation inputs and observing the resulting outputs‚ valuable insight may be obtained into which variables are most important and how variables interact. nz www.ncetianz.webs.com • Simulation can be used to experiment with new designs or policies prior to implementation‚ so as to prepare for what may happen. • Simulation can be used to verify analytic solutions
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Analysis of Financial Time Series Third Edition RUEY S. TSAY The University of Chicago Booth School of Business Chicago‚ IL A JOHN WILEY & SONS‚ INC.‚ PUBLICATION Analysis of Financial Time Series WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding‚ Noel A. C. Cressie‚ Garrett M. Fitzmaurice‚ Iain M. Johnstone‚ Geert Molenberghs‚ David W. Scott‚ Adrian F. M. Smith‚ Ruey S. Tsay‚ Sanford Weisberg Editors Emeriti:
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bounce was 30 inches and the standard deviation was ¾ inches. What is the chance of getting a “fast” standard ball? T otal no. of observations N = 100 Mean‚μ = 30inches Standard deviation‚ σ=3/4 inches=0.75 inches Suppose ’x’ is the normal variable=32 inches 4. Explain
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ILO6. compute probabilities for a normal distribution and determine normal scores from specific probability requirements. Syllabus 1. Data collection and sampling Data collection Taking a census Sampling Methods of selection a sample Simple random sample Systematic sampling Stratified sampling Summarizing Data Dot Diagrams Stem-and-Leaf Displays Frequency Distributions Graphical Presentations 2. 3. Statistical Descriptions Measures of Location The mean The weighted mean The median
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Probability Distribution • Confidence Intervals Calculations for a set of variables Open the class survey results that were entered into the MINITAB worksheet. We want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc > Row Statistics and select the radio-button corresponding to Mean. For Input variables: enter all 10 rows of the die data. Go to the Store result in: and select
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central The Central Limit Theorem A long standing problem of probability theory has been to find necessary and sufficient conditions for approximation of laws of sums of random variables. Then came Chebysheve‚ Liapounov and Markov and they came up with the central limit theorem. The central limit theorem allows you to measure the variability in your sample results by taking only one sample and it gives a pretty nice way to calculate the probabilities for the total ‚ the average and the proportion
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APPM 3570 — Exam #1 — February 20‚ 2013 On the front of your bluebook‚ write (1) your name‚ (2) 3570/EXAM 1‚ (3) instructor’s name (Bhat or Kleiber)‚ (4) SPRING 2013 and draw a grading table with space for 4 problems. Do only 4 of 5 problems. On the front of your blue book‚ write down which 4 problems you are attempting‚ if you do more than 4 problems‚ only the first 4 problems done will be graded. Correct answers with no supporting work may receive little or no credit. Start each problem on a new
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EG40JQ/12 UNIVERSITY OF ABERDEEN SESSION 2011 – 2012 Degree Examination in EG40JQ SAFETY AND RELIABILITY ENGINEERING Friday 20 January 2012 Notes: (i) (ii) 2.00 p.m. – 5.00 p.m. Candidates ARE permitted to use an approved calculator Data sheets are attached to the paper. Candidates should attempt all FIVE questions. REGULATIONS: (i) You must not have in your possession any material other than that expressly permitted in the rules appropriate to this examination. Where
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