1. In each case, list the elements of the sample space. ex: the result of a single coint toss. S = {heads, tails} (a) The set of integers between 1 and 50 that are divisible by 8. (b) An experiment consists of tossing a coin until a tail or three heads appear. (c) An experiment consists of rolling a die and then flipping a coin once if the number on the die was even, or twice if the die was odd. (d) Two jurors are selected from among 4 to serve in a court trial. (Usie the notation A1 , . . . , A4 to denote the jurors). (e) A ball is selected from an urn containing 4 red balls, 3 blue balls, and 2 yellow balls. 2. In each case, define the correspondence between the sample space and the random variable (r.v.) outcomes. ex: Let the r.v. X be the result of a single coin toss. ????1 :heads (a) Let the r.v. X be a randomly chosen number between 1 and 50 that is divisible by 8. (this is trivial) (b) Let the r.v. Y be the answer to the question: does X (above) end in 8? (c) Let the r.v. Z be the number of heads in the outcome of the experiment in question 1b). (d) Let the r.v. W denote the number of times the coin was flipped in question 1c). (e) Let the r.v. V denote whether all of the coin flips in question 1c) were tails. (f) Let the r.v. U denote the color of the single ball selected from the urn in question 1e. (g) Let the r.v. T denote whether or not the ball chosen from the urn in question 1e is red. 3. Define the probability mass function of each random variable in question 2). ex: If the r.v. X denotes the outcome of a single coin toss, then the p.m.f f (x) is defined by ????0.5 :x=1 X = 0 : tails f(x)= 0.5 :x=0

Subject | Mathematics |

Due By (Pacific Time) | 09/09/2013 12:00 am |

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