Homework-Ch-04-key

Homework-Ch-04-key - Chapter 4 Homework key [Over 72...

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1 Chapter 4 Homework key 2011/09/20 [Over 72 points] 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. d) [2 p.] Given an example of independent statistical experiments. Rolling two dice, or rolling one die twice. Drawing two cards from a deck, or two balls from an urn, with replacement (you replace the card or ball you drew on the first try, and shuffle, before your second try.) e) [2 p.] Given an example of non-independent statistical experiments. The usual state lottery setup: you have a bunch of numbered balls in an urn, you draw a sequence of balls without replacing the balls drawn. As you draw each ball, the probabilities for the following draws change. f) [2 p.] For two sets A and B, define the Union AB The union of two sets is defined as the (larger) set of items that belong to either A or B (or both). g) [2 p.] For two sets A and B, define the Intersection The intersection of two sets is defined as the (smaller) set of items that belong to both A and B .
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2 h) [2 p.] For set S and a subset A, define the Complement c Aor A If A is a subset of S, then the complement of A with respect to S is defined as the set of items that belong to S that are not in A . 414. [Ch. 4, 14 points] (Probability) a) [2 p.] You roll a die. What is the probability of rolling a 3 ? 1/6 b) [2 p.] You roll a die. What is the probability of rolling a 2 or a 3 ?
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Homework-Ch-04-key - Chapter 4 Homework key [Over 72...

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