Class 03 2014 01 30 Probability Sample Space

Class 03 -2014 -01 -30 Probability Sample Space Liquid precipitation (event E 2) No precipitation (event E 1) Frozen precipitation (event E 3) Venn Diagram: The Sample Space consists of three event categories: Together they are collectively exhaustive, but in this case event E 2 and E 3 are not mutually exclusive, they can happen at the same time. (this material was discussed in class but this slide was not shown during class) 1

Class 03 -2014 -01 -30 Probability Sample Space Compound event: Liquid precipitation (event E 2) Any of the possible events (E 1 OR E 2 OR E 3) No precipitation (event E 1) Frozen precipitation (event E 3) Another illustration of Probability : The Sample Space consists of three event categories: Together they are collectively exhaustive, but in this case event E 2 and E 3 are not mutually exclusive, they can happen at the same time. (this material was discussed in class but this slide was not shown during class) 2

Class 03 -2014 -01 -30 Axioms of Probability (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) 3

Class 03 -2014 -01 -30 Axioms of Probability (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) 4

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

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

Class 03 -2014 -01 -30 Albany Airport Weather data 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) Data can be obtained from http: //www. erh. noaa. gov/aly/Climate/Albany/Climate. ALB. htm 7

Class 03 -2014 -01 -30 Analysis of Daily Weather data Albany Airport - Dec 2013 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. 8