Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Lecture 9—Probability and Statistics Lecture 9—Probability and Statistics (Ch. 3)(Ch. 3)Monday January 28Monday January 28thth•Review: the axioms of probability theory•Independent events•Counting events – examples•Statistical distributionsReading: Reading: All of chapter 3 (pages 52 - 64)All of chapter 3 (pages 52 - 64)***Homework 3 due Fri. Feb. 1st*******Homework 3 due Fri. Feb. 1st****Assigned problems, Assigned problems, Ch. 3Ch. 3: 8, 10, 16, 18, : 8, 10, 16, 18, 2020Homework assignments available on Homework assignments available on web pageweb pageExam 1: Exam 1: Fri. Feb. 8th (in class), chapters 1-4Fri. Feb. 8th (in class), chapters 1-4The axioms of probability theoryThe axioms of probability theory1. pi ≥ 0, i.e. pi is positive or zero2. pi ≤ 1, i.e. pi is less than or equal to 13. For mutually exclusive events, the probabilities for compound events, i and j, add( )i ji jp p p+= +•Compound events, (Compound events, (ii + + jj): this means either event ): this means either event ii occurs, or event occurs, or event jj occurs, or both. occurs, or both.•Mutually exclusive: events Mutually exclusive: events ii and and jj are said to be mutually exclusive are said to be mutually exclusive if it is impossible for both outcomes (events) to occur in a single if it is impossible for both outcomes (events) to occur in a single trial.trial.The axioms of probability theoryThe axioms of probability theory1. pi ≥ 0, i.e. pi is positive or zero2. pi ≤ 1, i.e. pi is less than or equal to 13. For mutually exclusive events, the probabilities for compound events, i and j, add•In general, for In general, for rr mutually exclusive events, the probability that one mutually exclusive events, the probability that one of the of the rr events occurs is given by: events occurs is given by:1 2........rp p p p= + + +Independent eventsIndependent eventsExample:What is the probability of What is the probability of rolling two sixes?rolling two sixes?Classical probabilities:Classical probabilities:166p =Two sixes:Two sixes:1 1 16,66 6 36p = � =•Truly independent events always satisfy this property.•In general, probability of occurrence of r independent events is:1 2........rp p p p= � � �nixiStatistical distributionsStatistical distributions, wherei iiiin xx N nN= =��87 9 106Mean:nixiStatistical distributionsStatistical distributions87 9 106, wherei iiiin xx N nN= =��Mean:nixiStatistical distributionsStatistical distributions87 9 106, where limii i iiNnx p x pN��= =�Mean:N � �Statistical distributionsStatistical distributionsnixi16, where limii i iiNnx p x pN��= =�Mean:Statistical distributionsStatistical distributionsnixi16, where limii i iiNnx p x pN��= =�Mean:Statistical distributionsStatistical distributionsnixi16, where limii i iiNnx p x pN��= =�Mean:Statistical distributionsStatistical distributionsnixi16, where limii i iiNnx p x pN��= =�Mean:N � �Statistical distributionsStatistical distributionsnixi16( ) ( )2 2i iix p x xs = D = -�Standard deviation( )221( ) exp22x xp xss p� �-� �= -� �� ��Statistical distributionsStatistical distributionsGaussian distribution(Bell
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