lectexamp7 - Chapter 1 Lecture Examples 1 Find the area...

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Chapter 1 Lecture Examples 1. Find the area under the snc to the right of: z = 1 . 82 ; z = - 2 . 11 ; z = - 0 . 09 . 2. Find the area under the snc to the left of: z = 0 . 82 ; z = - 1 . 19 ; z = - 0 . 92 . 3. Find the area under the snc to the right of z = 1 . 4238 . 4. Find the area under the snc to the right of: z = 3 . 72 ; z = - 3 . 89 . 5. Find the area under the snc to the left of: z = - 3 . 90 ; z = 4 . 19 . 6. It is possible to purchase four-, eight-, ten-, twelve-, and twenty-sided dice on the inter- net, in addition to the usual six-sided dice. Does anyone in the class have experience playing with any of these? If so, does the ELC seem reasonable to you? 7. A CM has a sample space that consists of four elements, denoted: a, b, c and d. As- suming the ELC, find the probabilities of each of the following events. (a) A = { a } (b) B = { a,b } (c) C = { b,c,d } 8. Refer to the previous problem. Now, in- stead of the ELC, assume that the probabil- ities of a, b, c and d follow the ratio 9:3:3:1. (a) Determine the probabilities of the in- dividual outcomes a, b, c and d. (b) Calculate the probabilities of the events A , B and C given in the pre- vious problem. 9. You are given the following information: the events A and B are disjoint; P ( A ) = 0 . 40 ; and P ( B ) = 0 . 25 . Calculate the fol- lowing probabilities. (a) P ( A or B ) . (b) P ( A c ) . (c) P ( B c ) . 10. You are given the following information: P ( A ) = 0 . 25 ; P ( B ) = 0 . 45 ; P ( AB ) = 0 . 20 . Calculate P ( A or B ) . 11. What is wrong with each of the following? (a) P ( A ) = 0 . 20 ; P ( B ) = 0 . 55 ; and P ( AB ) = 0 . 25 . (b) P ( A ) = 0 . 60 ; P ( B ) = 0 . 55 ; and A and B are disjoint. 1

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Chapter 2 Lecture Examples 1. Consider a sample space with three mem- bers: 1, 2 and 3. Assume the ELC and i.i.d. trials. The following table helps to visual- ize 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) The nine entries in this table are 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 . 2. 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) The 25 entries in this table are equally likely. Define X = X 1 X 2 , the product of the num- bers obtained in the first two trials. 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:
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This note was uploaded on 10/23/2009 for the course STAT STATS 371 taught by Professor Professorwardrop during the Fall '09 term at University of Wisconsin.

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lectexamp7 - Chapter 1 Lecture Examples 1 Find the area...

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