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06 - BTRY/STSCI 4080 Homework 6 Due Date Problem numbers...

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BTRY/STSCI 4080 Homework # 6 Due Date: 10/21/10 Problem numbers beginning with P (e.g., P1) denote problems from the “PROB- LEMS” section; those beginning with T (e.g., T1) denote problems taken from the “THEORETICAL EXERCISES” section. 1. Ross: p 105, P45 2. Ross: p 105, P47 3. Ross: p 106, P52 4. Ross: p 106, P58 5. Ross: p 109, P76 6. Ross: p 109, P83 7. Ross: p 172, P2 8. Ross: p 173, P7 & P8 9. Ross: p 173, P10; note that the problem is really asking you to compute the probabilities P ( A i | B ), i = 1 , 2 , 3 where A i = { X = i } and B = { X > 0 } . 10. Ross: p 174, P16 11. Ross: p 174, P19 12. Consider the example on Slides 163-164 (see also Example 3.4.4h in the book). Let E denote the desired event (i.e., that 5 appears before 7). This problem explores the solution using conditional probabilities given on page 84 of the book. Parts (a)-(c) are easy if you’ve read the example; part (d) is new and verifies a key claim that is used to solve this problem. (continued next page)
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Let: F = the event that the first trial is a 5. G = the event that the first trial is a 7. H = the event that the first trial is neither a 5 nor a 7. (a) Carefully explain why F , G and H form a partition of the
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