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Unformatted text preview: 5A” I '1‘“ .. SA— —5 {gulls-w o’:' Name 50 ’UULW'IS V l ‘“ an '- E01311 370 ”wasn't-l @1" Quiz 6 Friday, February 17, 2012. John throws darts at a circular target centered at point (0,0) of radius 2 meters and is equally likely to hit any point in the target. This forms a joint uniform PDF within the circle. 1. (2 pts) What is the probability that a dart falls in the square described by points (0,0), (0,) 1) (1 (,,1) (10)? fSICJ‘J)’ = c = “1?; Let X be the distance of John‘s hit from the center. 2. (2 pts) Find the CDF for X. . 2 WWW“ “wit PCX— X): C ‘ Rom ext-circle v44". reams x = CWXZ = fl 4‘1 13‘ F (it): 0.1 '\‘("<0 :1. 511;) '1 3— %) .1 05152 1):"! 2‘): 2 )x 3. (2 pts) Find the PDF for X. {2(x)=d L20: 0’ ii x<0 dz 2.x) .F0_x$2 0J NCQ<x 4. (Epts) Find the mean of X. [[37 E: zf‘)4*'§ixzdx= ,szjozzg: We 5. (2 pts) Suppose that John’s scores for multiple dart throws are normally distributed with a mean of 10 and with standard deviation 2. What is the probability that he will score greater than 9 but less than than 13? You can leave your answer in terms of the standard normal CDF, @(y). @0310 ~35 (i?) wear) 25,900.!) ...
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