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Chapter 5 Notes (1)

Chapter 5 Notes (1) - mm This chlpter Introduces MIN bu...

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Unformatted text preview: mm This chlpter Introduces MIN bu quantify rlndorlmes. ow u n l: 7 The prooapi g of in egn is viewed as a numerical measure olthe dance that the event will occur. {LL-tossing a lair coin. Chance of getting head is sort. (=05) Randomness The possible outcomes are known, but it is uncertain whkh will occur ior any given observation. 5g; Rolling a die, Drawing cards from a dect Random Phenomenon For a random phenomenon, I lndlviduil nutznmes are unpredictable - With a large number of observations, predictable patterns occur . The proportion ol times that something happens is highly random and variable In the short run, but very predictable In the lung rim {Layne outcome at tosslnl a Fair min once is unpredictaole. However, in the long rim, when the coin is tossed 2 large number of tlmes, we can predict that the ratio (ii or times heads occurred: ii of times tails occurred] to be approxim ateiy i :1, [new use none or them is tavored over the other as the coin is lair) prooaoiiity or a nanriorn Phenomenon The probability or a particular outcome in a random phenomenon is the proportion of times that the outcome would occur In 3 Ion; run at the observations. u‘fhe prooaoiiity or gettinr heads when tnsslng a tan coin being it means that the proportion oi times heads would occur in a long run or the observations is x. The prooaoiiiry (change) or rain being 40% ior today means, out oi a iarre nurnoer oi days with similar atmospheric conditions like today, proportion of days that rain occurs is 0.4. Indlplndem Trials Dmerent trials of a random phenomenon are independent it the outcome or any one trial is not aflected lay the outcome olany athertrial. M Assume you have 4 A's oi 0,..Q, and Q - Drawing a card with replacement —~ independent triils. (The urd you get In the first draw does not lltefl who! you ran get in the second draw. Le. ll you [at V in the first draw, the change ol getting V in the second draw still remains to be x) - Drawing a card without replacement —. Not independent. [ll you get V in the first draw, the phone or letting V in the second draw I! 0. So what you [In in "it first draw has aficted the chances at what you can get |n the second draw) WW Two terms relatedto probabilities are Introduced here. I SampleSpace ' Event sample space For a random phenomenon, the sample space is the set or all possible outcomes. M Roll : die unce Sample Spore : ( Tossing two coins Sample Space = ((H. H). (H, T). (7. H). (T. 7)} There was a blind test to identify three types of beer (A, B. C) by tasting them. If the Interested random inr'tabie ls number ol correct identifications, list out the sample space. (three cups contain three different beers and they test all three beta re they know the result). 5 = {0,1 ,3) Explanation: it is possible that you do not identify any olthe three correctly, or get one or them nonectty and the other two incorrect or get all three correct. But you cannot identify two rorrcctiy and get the other one wrong, (idenrilying two correctly means the third one automatically becomes correct) rrent An event is a subset otthe sample space. Eli: Refer to the use :11 rolling a die lEx 5) Event of rolling u even number = (2.4.6) Event of rolling a multiple of 3 = (3.6] Referring to the tossing or two wins Event of getting at least one heads = ((H.H),(H.T).(T,H)) Event of getting exactly one head = ((H, r). (T, H )) ...
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