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**Unformatted text preview: **Stat 0302B Business Statistics Spring 2010-2011 Chapter II Probability § 2.1 Introduction Probabilities are quantitative expressions of uncertain about a person’s knowledge of the occurrences of some events. We are all familiar with the term “chance”, or “probability”. “What is the probability that Arsenal will win the Premier League Championship 2011?” “If I spend more time studying in this semester, what is my probability of getting a higher GPA than the last semester? “Given a particular economic status, how likely is that the RMB will appreciate by more than 5 percent?” “What is the chance that a middle-aged person will spend more than $10000 in departmental stores per month?” “What is the probability of producing a defective product by a certain manufacturing line? Probability and Statistics Probability : deductive reasoning • From a known population to the unknown sample Statistical Inference : inductive reasoning • Using an observed sample to make a statement about the unknown population Population Sample Population Sample P.29 Stat 0302B Business Statistics Spring 2010-2011 Probability 1. Complete information about the population. 2. Sampling. 3. Make statement about the sample. Statistical Inference 1. Incomplete information about the population. 2. Sampling. 3. Observed sample. 4. Make statement about the population. Example 2.1 Probability Calculation Statistical Inference _ 1. We have a fair coin . W e h a v e a c o i n . (i.e. ( ) ( ) 5 . = = Tail P Head P ) 2. The fair coin is tossed ten times. This coin is tossed ten times. 3. P (all are head) = ? All are head. 4 . I s i t a f a i r c o i n ? From probability calculation, if the coin is fair, then P (all are head) < 0.001. If it is a fair coin, it is very unlikely to observe ten heads in a row. Therefore based on the observation of ten heads, we may infer that the coin is not a fair coin Terminology and Notation Experiment : A process whose result can not be predicted with certainty prior to the observation (measurement). Outcome : A possible result of the experiment that cannot be decomposed. e.g. Outcome of rolling a die: 1, 2, 3, 4, 5, 6 Sample Space : A collection of all outcomes that could occur in an experiment. Event : A statement about the result of an experiment, which can be expressed as a collection of one or more outcomes. e.g. “My new born baby is a boy.” Notation: , , … (e.g. 1 E 2 E Boy E = 1 , Girl E = 2 , etc) P.30 Stat 0302B Business Statistics Spring 2010-2011 Probability : A measure of how likely an event is to occur when the experiment is run. Notation : ( ) E P Mutually Exclusive : A group of events are said to be mutually exclusive if when one event occurs, the other cannot occur....

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