homework6b - Due 9/10 Chapter 1 Homework 1 Find the area...

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Due 9/10: Chapter 1 Homework 1. Find the area under the snc to the right of: z = 2 . 18 ; z = 3 . 15 ; z = 0 . 096 . 2. Find the area under the snc to the left of: z = 2 . 52 ; z = 1 . 82 ; z = 0 . 923 . 3. 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 } . 4. Refer to the previous exercise. Assume the ELC. Calculate the probability of each of the events, A , B and C . 5. A CM has a sample space that consists of five outcomes: 1, 2, 3, 4 and 5. For 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 , P (3) = 0 . 25 , P (4) = 0 . 20 , P (5) = 0 . 10 . (b) P (1) = 0 . 30 , P (2) = 0 . 15 , P (3) = 0 . 20 , P (4) = 0 . 20 , P (5) = 0 . 10 . (c) P (1) = 0 . 30 , P (2) = 0 . 15 , P (3) = 0 . 25 , P (4) = 0 . 20 , P (5) = 0 . 20 . (d) P (1) = 0 . 30 , P (2) = 0 . 15 , P (3) = 0 . 25 , P (4) = 0 . 40 , P (5) = 0 . 10 . 6. 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 } . 7. Refer to the previous exercise. (a) Verify that: P ( B or D ) negationslash = 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 , explain why you know that P ( A ) = 0 . 65 without adding the probabilities of outcomes 1, 3 and 5. (d) Of the five events listed in Exercise 6, find all pairs that illustrate Rule 5. 8. You are given the following information: the events A and B are disjoint; P ( A ) = 0 . 30 ; and P ( B ) = 0 . 55 . Calculate the fol- lowing probabilities. (a) P ( A or B ) . (b) P ( A c ) . (c) P ( B c ) . 9. You are given the following information: P ( A ) = 0 . 65 ; P ( B ) = 0 . 45 ; P ( AB ) = 0 . 30 . Calculate P ( A or B ) . 1
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Due 9/17: Chapter 2 Homework 1. Consider a sample space with five mem- bers: 0, 1, 2, 3 and 4. Assume the ELC and i.i.d. trials. The following table helps to visualize the results of the first two trials: X 2 X 1 0 1 2 3 4 0 (0,0) (0,1) (0,2) (0,3) (0,4) 1 (0,1) (1,1) (1,2) (1,3) (1,4) 2 (0,2) (2,1) (2,2) (2,3) (2,4) 3 (0,3) (3,1) (3,2) (3,3) (3,4) 4 (0,4) (4,1) (4,2) (4,3) (4,4) Define X = X 1 + X 2 , the total of the num- bers obtained in the first two trials. Find the sampling distribution of X . 2. Consider a sample space with three mem- bers: 1, 2 and 3. Assume the ELC and i.i.d. trials. Define X = X 1 + X 2 + X 3 , the total of the numbers obtained in the first three tri- als. Find the sampling distribution of X . 3. Consider a sample space with three mem- bers: 1, 2 and 3. Do not assume the ELC. Instead assume the following: P (1) = 0 . 4 , P (2) = 0 . 2 and P (3) = 0 . 4 . Assume i.i.d. trials. The following table helps to visualize the results of the first two trials: X 2 X 1 1 2 3 1 (1,1) (1,2) (1,3) 2 (2,1) (2,2) (2,3) 3 (3,1) (3,2) (3,3) Note that these nine entries are not equally likely. Define X = X 1 + X 2 , the total of the num- bers obtained in the first two trials. Find the sampling distribution of X .
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