Exam-2-Universe-Ch4-A

Exam-2-Universe-Ch4-A - BUS-271 Exam-2 Universe Answers...

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1 BUS-271 Exam-2 Universe Answers 2011-09-21 CHAPTER 4 401. [Ch.4, 10 p.] (Definitions) a. [2 p.] Define what we mean by the “sample space” for a statistical experiment. The sample space for a statistical experiment is the set of possible outcomes of the experiment. (Example: for rolling a die, it is {1,2,3,4,5,6}.) b. [2 p.] What do we mean when we say that two statistical experiments are independent? Two statistical experiments are independent when the outcome of one does not depend on the outcome of the other e.g. when you flip a coin twice, the result the second time does not depend on the result you got on the first flip. c. [2 p.] If I flip a coin twice, are those two statistical experiments independent or not? Yes, independent. d. [2 p.] If I draw cards from a normal deck and replace the card between draws, are these statistical experiments independent or not? Yes, selection with replacement results in independent trials. e. [2 p.] If I draw balls from an urn without replacement, are these statistical experiments independent or not? No, selection without replacement does not yield independent trials: if you draw ball #78 in the first draw, that ball cannot be drawn in the second trial.

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2 402. [Ch. 4; 12 points] (Definitions: Set theory) Given the following Venn diagram: (a) [2 p.] list the members of set A. A = { a, b, c, d, i, j } (b) [2 p.] list the members of set B. B = { c, d, e, f } (c) [2 p.] list the members of A B. { , } A B c d Intersection: this is the list of items or units that are both members of A and of B.
3 (d) [2 p.] What is P(A) ? Assume Classical probability. P(A) = |A| / |S| = 6 / 10 = 0.6 The probability of any set is equal to the number of members of tha t set divided by the number of members in the “world” set S. [In terms of our probability problems: the probability of a particular outcome or set of outcomes of an experiment is equal to the number of outcomes that fit our desired description, divided by the total number of outcomes (sequences or groups) possible.] (e) [2 p.] What is P(A B)? | | 8 ( ) 0.8 | | 10 AB P A B S (f) [2 p.] What is P( (A B) C ) ? ( ) 1 ( ) 1 0.8 0.2 () c P P A B     This is because: (a) the complement of a set A is the set of all items that are in S that are NOT in A; and (b) if the probability of S is always 1, then the probability of A c must be equal to 1 P(A).

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4 403. [Chapter 4; 16 p.] (Definitions) a) [2 p.] What is a statistical experiment? A natural or artificial process which produces, each time it is invoked, one outcome out of a small set of possible outcomes, with a specific probability distribution. b) [2 p. ] What is the “sample space” for a statistical experiment? The sample space is the set of possible outcomes of the experiment. c) [2 p. ] What do we mean by “independent” statistical experiments? If we do the same experiment twice in a row, the probabilities of the different outcomes on the second try are not influenced by whatever happened on the first try. If we carry out two different experiments, the outcomes of one are not affected by whatever outcome resulted from the other.
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Exam-2-Universe-Ch4-A - BUS-271 Exam-2 Universe Answers...

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