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1 Venn Diagram: The Sample Space consists of three event categories: Together they are collectively exhaustive, but in this case event E2 and E3 are not mutually exclusive, they can happen at the same time. Class 03 -2014-01-30 No precipitation (event E1) Liquid precipitation (event E2) Frozen precipitation (event E3) Sample Space (this material was discussed in class but this slide was not shown during class)

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2 Another illustration of Probability : The Sample Space consists of three event categories: Together they are collectively exhaustive, but in this case event E2 and E3 are not mutually exclusive, they can happen at the same time. Class 03 -2014-01-30 No precipitation (event E1) Liquid precipitation (event E2) Frozen precipitation (event E3) Sample Space Compound event: Any of the possible events (E1 OR E2 OR E3) (this material was discussed in class but this slide was not shown during class)

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3 Class 03 -2014-01-30 (1)The probability of any event is nonnegative (2)The probability of the compound event is 1 (3)The probability of one or the other of two mutually exclusive events is the sum of the individual probabilities. (this material was discussed in class but this slide was not shown during class)

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4 Class 03 -2014-01-30 (1) 0≤ P(E) ≤ 1 (2) P(S) = 1 (3) P(E 1 or E 2 ) = P(E 1 ) +P(E 2 ), but only if E 1 and E 2 are mutually exclusive events, i.e. P(E 1 and E 2 ) = 0 (this material was discussed in class but this slide was not shown during class)

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5 Class 03 -2014-01-30 (1) The probability of the complement event: P(E c ) =1 – P(E) (this material was discussed in class but this slide was not shown during class)

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Class 03 -2014-01-30 6 Data can be obtained from http://www.erh.noaa.gov/aly/Climate/Albany/ClimateALB.htm For each month since 1996 temperatures, wind, precipitation, … (Historical data archives are stored In other archives)

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Class 03 -2014-01-30 7 Data can be obtained from http://www.erh.noaa.gov/aly/Climate/Albany/ClimateALB.htm Example page: Table with December 2013 data This is embedded into HTML web page and it requires extra work to prepare data for statistical analysis. (Notepad, EXCEL)

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8 Class 03 -2014-01-30 Filename: KALB_201312.csv We will learn to read data-tables into R Using parts of the data table by use of column names Create simple plots Create a first loop in the program Use if-else statements for flow control in the program And we will begin with the exploratory data analysis: Frequentist’s approach to probability and applying the arithmetic mean to obtain a monthly mean temperature from daily data samples.

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AP Statistics Section 6.2 B Probability Rules. If A represents some event, then the probability of event A happening can be represented as _____.

AP Statistics Section 6.2 B Probability Rules. If A represents some event, then the probability of event A happening can be represented as _____.

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