midterm 2004

midterm 2004 - (c) the probability that the coin is the 112...

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STATS 116: Midterm Examination July 21st, 2004 S//,ow all ulork. Justify your assertions.
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Question 1 [20 points] Five cards are dealt from a standard deck of 52. Write down numerical expressions for: (a) the probability that all cards are of the same suit; (b) the probability that two or more are aces.
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Question 2 [20 points] Suppose that the cumulative distribution function of the random variable X is given by ( 0, x 5 0 (a) Find thc probability density furictioii of X. (b) Find a ~ilimerical expression for P(3 < X < 5).
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Question 3 [20 points] Joe has two coins. One coin shows heads with probability 1/10 when spun, and the other shows heads with probability 112. Suppose Joe picks one of the two coins at random and spins it twice. Find: (a) the probability that the first spin shows heads; (b) the probability that both spins show heads;
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Unformatted text preview: (c) the probability that the coin is the 112 coin give11 heads on both spins. Question 4 [20 points] A student answers a set of 100 truelfalse questions by answering 36 cor- rectly, and guessirig the other 64 at random. (a) If the passing score is 70 or more correct answers, what is the approxi- mate probability that the student passes the exam'! Give your answer as a decimal correct to two places - (b) Another student also knows 36 correct answers and guesses the rest of the questions at randorn. What is the approximate probability that exactly one of these two students passes the examination? Question 5 [20 points] Determine the number of vectors (xl, 2 2 , . . . , x,) such that each xi is a posi- tive integer (i.e. xi &gt; 0) and where r &lt; 72....
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midterm 2004 - (c) the probability that the coin is the 112...

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