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Probability and Probability Distributions What is Probability ? • If we toss a fair coin, there are two possible outcomes, a head (H) or a tail (T); that is N=2. So the P(H) = ½ ……(0.5). • If a toss of two coins, how many possible outcomes ? First coin Second coin H T H T H T Possible outcomes : HH, HT, TH, TT What is the probability of : - P(2H) - P (at least 1H) -P( 1H and 1T) • A pregnant woman wonders about the chance of having a boy or a girl baby. Vital statistics datas indicate there are about 1056 live births of boys for every 1000 live birth of girls, so she estimate her probability of having a boy as 1056 / 2056 = 0.514 Probability : • Probability applies exclusively to a future event, never to a past (outcome of event is unknown) • Probability may be used to measure the uncertainty of the outcome of such events, for example , the probability of surviving to age 80 of developing cancer • Probability statements are Numeric, in the range of 0 – 1 ( 0: the event will not happen, 1 the event will happen with certainty) Events : • • • • Mutually exclusive event Not mutually exclusive event Complementary event Independence event Mutually exclusive event : • Event that cannot happen simultaneously, that is, if one event happen, the other event cannot happen • For example : toss a coin, baby born (boy or girl) • P(A or B) = P(A) + P(B) • P (A U B)…..P(A union B) Not mutually exclusive event : • Two event can happen simultaneously, so a part of two events are intersection • For example : the event A that a 30 year old woman lives to see her 70th birthday and the event B that 30 years old husband is still alive at age 70. A and B would be the event that both the 30 year-old woman and her husband are alive at age 70. Not mutually exclusive event : • P(A or B) = P(A) + P(B) – P(AB) Event A AB Event B • P(both A and B) = P(A)xP(B) Complementary event • Event Ac is the complement of event A A Ac • For example : 100 patients Lung cancer, 20 patients still a live for 3 years….P(A) = 20/100 = 0.2), so that 80 patients Acdied for 3 year 0.8)……1 – P(A) )=80/100 = P( Independent event • Two events are independent if the occurrence of one has no effect on the chance of occurrence of the other. • The multiplication rule • For example : the outcomes of repeated tosses of a coin, because the outcomes of one toss does not affect the outcomes of any future toss. Probability Distributions • A key application of probability to statistics is estimating the probabilities that are associated with the occurrence of different events. • Help us reach a decision whether certaint events are significant or not • Mathematical distributions Probability Distributions • Variables continue – Normal Distributions – Sample Mean Distributions ( t- student distributions) – F Distributions • Variables discrete : – Binomial distributions – Chi Square distributions the Normal Distribution Properties : • Symmetrical Bell shaped curve extending infinitely in both directions • Have area under the curve. The total is 1 • It is a theoretical distribution defined by two parameters: µ and • The mean and median of a Normal Distribution are equal (Kuzma, 2005; p. Area under the Normal Curve 99,74% 95,45% 68,26% 200 800 µ-3 µ+3 300 µ-2 400 µ-1 500 µ 600 700 µ+1 µ+2 (Kuzma, 2005; p. DATA YG MEMILIKI DISTRIBUSI MENDEKATI DISTRIBUSI NORMAL • Sebagian besar data yg berasal dari hasil pengukuran variabel kuantitatif ( interval , ratio ); • Sampling distribution of any quantitative data with n ≥ 30; • Sampling distribution of data from dummy variables (yes or no, 0 or 1, etc) in which p x n ≥ 5.00. – Examples n


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