f2011homework14-2

f2011homework14-2 - (c) C = cfw_4. Chapter 1 Homework; FALL...

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Chapter 1 Homework; FALL 2011 1. Consider the following CM: A 10-sided die is tossed, with faces marked 1, 2, . .., 10. The outcome is the number on the face that lands up. (a) Determine the sample space. (b) List the elements of the following event: A = the outcome is an odd number. (c) List the elements of the following event: B = the outcome is an even number larger than 6. (d) Describe the following event in words: C = { 7 , 8 , 9 , 10 } . 2. Refer to the previous exercise. Assume the ELC. Calculate the probability of each of the events, A , B and C . 3. A CM has a sample space that consists of Fve outcomes: 1, 2, 3, 4 and 5. ±or each of the following assignments, decide whether it is a mathematically valid way to assign probabilities for this situation. If not, ex- plain why not. (a) P (1) = 0 . 30 ,P (2) = 0 . 15 (3) = 0 . 25 (4) = 0 . 20 (5) = 0 . 10 . (b) P (1) = 0 . 30 (2) = 0 . 15 (3) = 0 . 20 (4) = 0 . 20 (5) = 0 . 10 . (c) P (1) = 0 . 30 (2) = 0 . 15 (3) = 0 . 25 (4) = 0 . 20 (5) = 0 . 20 . (d) P (1) = 0 . 30 (2) = 0 . 15 (3) = 0 . 25 (4) = 0 . 40 (5) = - 0 . 10 . 4. Refer to the previous exercise. Use assign- ment (a) to calculate the probability of each of the following events. (a) A = { 1 , 3 , 5 } . (b) B = { 2 , 4 } . (c) C = { 4 } . (d) D = { 3 , 4 , 5 } . (e) E = { 1 , 3 } . 5. Refer to the previous exercise. (a) Verify that: P ( B or D ) ± = P ( B )+ P ( D ) . (b) Verify that Rule 6 is true for events B and D . (c) Given that P ( B )=0 . 15 + 0 . 20 = 0 . 35 ,e x p l a i nw h yy o uk n o wt h a t P ( A . 65 without adding the probabilities of outcomes 1, 3 and 5. (d) Of the Fve events listed in Exercise 4, Fnd all pairs that illustrate Rule 5. 6. You are given the following information: the events A and B are disjoint; P ( A )= 0 . 30 ;and P ( B . 55 .Ca lcu la tethefo l - lowing probabilities. (a) P ( A or B ) . (b) P ( A c ) . (c) P ( B c ) . 7. You are given the following information: P ( A . 65 ; P ( B . 45 ; P ( AB 0 . 30 te P ( A or B ) . 1
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Chapter 1 Homework Continued 8. Consider a sample space with fve mem- bers: 0, 1, 2, 3 and 4. Assume the ELC and i.i.d. trials. Defne X = X 1 + X 2 ,theto- tal oF the numbers obtained in the frst two trials. ±ind the sampling distribution oF X . 9. Consider a sample space with three mem- bers: 1, 2 and 3. Assume the ELC and i.i.d. trials. Defne X = X 1 + X 2 + X 3 ,theto ta lo F the numbers obtained in the frst three tri- als. ±ind the sampling distribution oF X . 10. Consider a sample space with Four mem- bers: 1, 2, 3 and 4. Do not assume the ELC. Instead assume the Following: P (1) = 0 . 1 ,P (2) = 0 . 2 (3) = 0 . 3 and P (4) = 0 . 4 . Assume i.i.d. trials. Defne X = X 1 + X 2 , the total oF the numbers obtained in the frst two trials. ±ind the sampling distribution oF X . 11. ReFer to the previous question. Defne X = X 1 + X 2 + X 3 Fthenumbe r s obtained in the frst three trials. ±ind the sampling distribution oF X . 12. ReFer to the table in problem 10 oF the Chapter 1 Lecture Examples. (a) VeriFy (i.e. count 5-tuples and then di- vide) my statement that P ( X =7)= 0 . 00193 . (b) VeriFy (i.e. count 5-tuples and then divide) my statement that P ( X = 27) = 0 . 00450 . (c) VeriFy the nearly certain interval I give For P ( X =17) . (d) VeriFy the nearly certain interval I give For P ( X =23) .
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This note was uploaded on 12/10/2011 for the course STATS 371 taught by Professor Hanlon during the Fall '11 term at Wisconsin.

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f2011homework14-2 - (c) C = cfw_4. Chapter 1 Homework; FALL...

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