Problem Set #8 in IE 342 Mechanical Engineering at University of Illinois at Chicago, Assignments of Probability and Statistics

Download Problem Set #8 in IE 342 Mechanical Engineering at University of Illinois at Chicago and more Assignments Probability and Statistics in PDF only on Docsity! UNIVERSITY OF ILLINOIS AT CHICAGO Mechanical Engineering IE 342 Michael J. Scott Spring 2001 Problem Set #8 Issued: 14 Apr 2001 Due: 25 Apr 2001 Reading: Walpole, Ch. 9 1. To answer this question, you will need software. MATLAB, Maple, and Microsoft Excel all have the necessary capabilities, and there are others. Any one that works is fine. Collaboration on this problem is strongly encouraged — the point is for you to learn to use the software properly. In general, the functions you will need are called things like tcdf, tdist, tinv, fcdf, finv, fdist, chi2inv, chi2dist, chi2cdf. Some programs use α, others 1 − α (in other words, if α = 0.1 on the given table, your program may be looking for 0.1, and may be looking for 0.9). (a) In Table A.4 in Walpole, we see that tα,ν = 0.906 when α = 0.20 and ν = 6. What is the required syntax to recreate this result in the program you are using? (b) On the same table, we see that if ν = 5 and tα,ν = 2.015, then α = 0.05. What do you have to do to get this result with your program? (c) To six decimal places, what is t0.24,7? (d) To six decimal places, if tα,12 = 3.00, what is α? (e) Now consider Table A.5. What is χ2 0.015,10 ? Include the syntax your program requires to get this answer. (f) What value of α yields χ2 α,10 = 3.0? Again, include the required syntax. (g) Now consider Table A.6. Note that f0.05,4,9 = 3.63. What do you need to do with your program to recreate this if α = 0.05, ν1 = 4, and ν2 = 9 are given? What if fα,4,9 = 3.63 is given, and you wish to find α? (h) Given ν1 = 4, ν2 = 9, and α = 0.02. What is fα,ν1,ν2? (i) Given ν1 = 4, ν2 = 9, and fα,ν1,ν2 = 2.0. What is α? 2. Walpole, p. 287, Prob. 3. 3. Walpole, p. 287, Prob. 6. 4. Walpole, p. 288, Prob. 7. 5. Walpole, p. 288, Prob. 9. 6. (Extra Credit) Walpole, p. 286, Prob. 1. 1