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Let the random variable X denote the number of semiconductor wafers that need to be analyzed in order to detect a large particle of contamination. Assume that the probability that a wafer contains a large particle is 0.01 and that the wafers are independent. Determine the probability distribution of X. Let p denote a wafer in which a large particle is present, and let a denote a wafer in which it is absent. The sample space of the experiment is infinite, and it can be represented as all possible sequences that start with a string of a s and end with p. That is, s 5 p, ap, aap, aaap, aaaap, aaaaap, and so forth6 12 P1p2 0.01. Also, using the inde-

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Consider a few special cases. We have P1X pendence assumption P1X A general formula is P1X x2 P1aa p ap2 1x 12a s 0.99x

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Flanagan, D P, & Ortiz, S O (2001) Essentials of cross-battery assessment New York: Wiley Flanagan, D P, Ortiz, S O, Alfonso, V C, & Mascolo, J T (in press) The Achievement test desk reference (ATDR): Comprehensive assessment and learning disabilities Boston: Allyn & Bacon Flaugher, R L (1978) The many definitions of test bias American Psychologist, 33, 671 679 Fletcher, J M, Francis, D J, Shaywitz, S E, Lyon, G R, Foorman, B R, Stuebing, K K, & Shaywitz, B A (1998) Intelligent testing and the discrepancy model for children with learning disabilities Learning Disabilities Research & Practice, 13, 186 203 Flor-Henry, P (1976) Lateralized temporal-limbic dysfunction and psychopathology Annals of New York Academy of Sciences, 280, 777 795 Flynn, J R (1983) Now the great augmentation of the American IQ Nature, 301, 655 Flynn, J R (1984).

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Describing the probabilities associated with X in terms of this formula is the simplest method of describing the distribution of X in this example. Clearly f 1x2 0. The fact that the sum of the probabilities is 1 is left as an exercise. This is an example of a geometric random variable, and details are provided later in this chapter.

The mean IQ of Americans: Massive gains 1932 to 1978 Psychological Bulletin, 95, 29 51 Flynn, J R (1986) Sociobiology and IQ trends over time Behavioral and Brain Sciences, 9, 192 Flynn, J R (1987) Massive gains in 14 nations: What IQ tests really measure Psychological Bulletin, 101, 171 191 Flynn, J R (1998a) IQ gains over time: Toward finding the causes In U Neisser (Ed), The rising curve: Long-term gains in IQ and related measures (pp 25 66) Washington, DC: American Psychological Association Flynn, J R (1998b) Rising IQ scores: Implications for the elderly Australian Journal on Ageing, 17, 106 107 Flynn, J R (1998c) WAIS-III and WISC-III IQ gains in the United States from 1972 to 1995: How to compensate for obsolete norms Perceptual and Motor Skills, 86, 1231 1239 Fogel, M L (1965) The Proverbs Test in the appraisal of cerebral diseases.

The following structure shows the elements of CHECK POINT (287):

EXERCISES FOR SECTION 3-2

Journal of General Psychology, 72, 169 275 Forsyth, A, Gaddes, W J, Reitan, R M, & Tryk, H E (1971) Intellectual deficit in multiple sclerosis as indicated by psychological tests (Research Monograph No 23) Victoria, BC, Canada: University of Victoria Fowler, P C, Richards, F C, & Boll, T J (1980) WAIS factor patterns of epileptic and normal adults Journal of Clinical Neuropsychology, 2, 115 123 Fowles, G P, & Tunick, R (1986) WAIS-R and Shipley estimated IQ correlations Journal of Clinical Psychology, 42, 647 649 Foy, A, O Connell, D, Henry, D, Kelly, J, Cocking, S, & Halliday, J (1995) Benzodiazepine use as a cause of cognitive impairment in elderly hospital inpatients Journal of Gerontology: Medical Sciences, 50, 99 106 Fraboni, M, Saltstone, R, Baines, G H, & Cooper, D (1988).

3-13 The sample space of a random experiment is {a, b, c, d, e, f }, and each outcome is equally likely A random variable is defined as follows: outcome x a 0 b 0 c 15 d 15 e 2 f 3 probability 05, a storage device with 500 gigabytes capacity will sell with a probability 03, and a storage device with 100 gigabytes capacity will sell with probability 02 The revenue associated with the sales in that year are estimated to be $50 million, $25 million, and $10 million, respectively Let X be the revenue of storage devices during that year Determine the probability mass function of X 3-21 An optical inspection system is to distinguish among different part types The probability of a correct classification of any part is 098.

Single Access Point Check Point uses for I&A enterSystem session per client identify(client) authenticate(client,credential) isallowed(client) implements Concrete Check Point session per client identify(client) authenticate(client,credential) isallowed(client)

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