STAT 410 Midterm: STAT410 DOLGOPYAT-D FALL2007 0101 MID EXAM 1

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Note if you can not solve say part (a) for one of the problems you still get credit for other parts. Answers like let x be the answer for part (a) then the answer for part (b) is 4!x 5! are allowed. (1) a matchbox contains 20 brown and 10 yellow matches. 0 if x [0, 1] otherwise (a) find the value of c and compute the cumulative distribution func- tion of x. (b) let x1, x2, x3, x4 be mutually independent and have the same distribution as x. Find the cumulative distribution function of y. (c) let x1j, x2j, x3j, x4j, j = 1 . 5 be mutually independent and have the same distribution as x. Find the probability that exactly 3 among those numbers will take value between 1/4 and 3/4. (3) 26 cards are chosen from a standard deck of 52 cards.

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