Chpt05 - Chapter 5 Probability and Sampling Distributions...

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Chapter 5 Probability and Sampling Distributions Section 5.1 1. (a) Sampling without replacement means that no repeated items will occur in any sample. There are 10 possible such samples of size 3: {a,b,c}, {a,b,d}, {a,b,e}, {a,c,d}, {a,c,e}, {a,d,e}, {b,c,d}, {b,c,e}, {b,d,e}, {c,d,e}. As you learned in the discussion of the binomial distribution, the number of ways to choose a sample of 3 distinct items from a list of 5 items is given by = 10, which shows that the list above is indeed complete. 3 5 (b) A contains 3 samples from the list in (a); i.e., A = { {a,b,c}, {a,c,d}, {a,c,e}} (c) The complement of A is A = {{a,b,d}, {a,b,e}, { {a,d,e}, {b,c,d}, {b,c,e}, {b,d,e}, {c,d,e}} 2. A Venn diagram of these three events is (a) The event ‘at least one plant is completed by the contract date’ is represented by the shaded area covered by all three circles:
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Chapter 5 Probability and Sampling Distributions 2 (b) The event ‘all plants are completed by the contract date’ is the shaded area where all three circles overlap: (c) The event ‘none of the plants is completed by the contract date’ is the complement of the shaded area in (a): (d) The event ‘only the plant at site 1 is completed by the contract date’ is shown shaded:
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Chapter 5 Probability and Sampling Distributions 3 (e) The event ‘exactly one of the three plants is completed by the contract date is: (f) The event ‘either the plant at Site 1 or Site 2 or both plants are completed by the contract date’ is: 3. To envision the events A and B, it helps to draw a number line with the integers representing the possible numbers of defective items: 1 2 3 4 5 6 7 8 9 10 A B (a) The event A and B consists of the integers {4, 5}. That is, A and B is the event ‘either 4 or 5 defectives in the sample’.
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Chapter 5 Probability and Sampling Distributions 4 (b) The event A or B consists of all ten integers. There are many ways to describe this event. One description of A or B is the event ‘there is at least one defective in the sample’. (c) The complement of A consists of the integers {1, 2, 3}. In words, A is the event ‘there are at most 3 defectives in the sample’. 4. Any two events A and B for which (1) A and B are disjoint and (2) the event A or B does not coincide with the entire sample space will be such that P(A) + P(B) 1. Representing events A and B by circles, this means that any two non-overlapping circles whose combined area does not equal 1 will satisfy the requirements of this problem: 5. The tree diagram is shown below. Note that it is not necessary for all the branches to be of the same length. That is, some branches may stop early in the tree, while others may extend through several additional branching points. meet standards meet standards do not meet standards scrap scrap readust crimp
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Chapter 5 Probability and Sampling Distributions 5 6. The tree diagram is: Bit sent Bit received 0 1 0 1 0 1 7. The event A and B is the shaded area where A and B overlap in the following Venn diagram. Its complement consists of all events that are either not in A or not in B (or not in both).
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This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue.

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Chpt05 - Chapter 5 Probability and Sampling Distributions...

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