STAT 1053 Week 4
STAT 1053 Week 4 STAT 1053
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This 3 page Class Notes was uploaded by Morgan Routman on Wednesday February 4, 2015. The Class Notes belongs to STAT 1053 at George Washington University taught by Professor Balaji in Winter2015. Since its upload, it has received 102 views. For similar materials see Intro to Statistics for Social Sciences in Statistics at George Washington University.
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Date Created: 02/04/15
STAT 1053 Week 4 Chapter 3 2415 948 PM 0 Study of randomness and uncertainty 0 The numerical measurement of chance 0 Ie probability of getting heads in a coin toss Types of Probability PEvent the relative frequency of the event a Law of Large Numbers 0 When an experiment is repeated a large number of times with the same conditions then the relative frequency of a particular outcome will approach the actual frequency Basic outcomes are defined Probabilities are assigned to those outcomes With these assignments probabilities of compound events can be computed Process that yields a certain outcome 0 Any basic outcome of an experiment 0 Set of all possible outcomes of an experiment 0 A subset Example Toss a coin three times There are 8 possible outcomes 2 outcomes per occurrence and three occurrences therefore 2 x 2 x 2 8 Sample Space S HHH HHT HTH THH HTI39 THT 39l l39H 39ITI39 8 A Event A exactly two heads show up HHT HTH THH o All sample point probabilities must lie between 0 and 1 o Probabilities of the same event must add up to 1 o The sum of all of the probabilities of sample points in event A must equal event A Example Consider the Sample Space abcde Pa 03 PbPc015 Pd02 A abc B de C be Find Pe PA PB PC 03015015015 1 08 02 Pe 03015015 06 PA 0202 04 PB 01502 035 PC 08 o If all of the outcomes are equally probable then the probability of the event can be shown by PA nAnS Where nA the number of sample points in the event and nS number of sample points in S o If stages are done in stages they are independent You can multiply the outcomes of each stage to see the possible outcomes for the entire experiment read as factorial nn1n2 0 Always 1 Example 5 5x4x3x2x1 120 STAT 1053 Week 4 Continued 2415 948 PM o Ordered arrangement 0 the number of permutations of n distinct objects at r times 0 Unordered subset Example 10P3 10103 10x9x8x7l7 720 Can also be done on the calculator using the nPr function Example 10C3 103 10P33 7206 120 0 Can be used to determine the nCr top number denotes the row bottom the number within the row 0 Use the number of letters in volume 0 VOLUME 6 720 o How many arrangements can we get that start with e After e there are five spots therefore the answer is 5 120 o What is the probability that the word made from the letters starts with a vowel Starts with o 5 120 Starts withu 5 120 120x120x120 360 720 05 50
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