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Unformatted text preview: Administration I Homework 11 Due Tuesday at 5:00 PM CS70: Satish Rao: Lecture 31. Continuous Probability 1. Motivation. 2. Continuous Random Variables. 3. Cumulative Distribution Function. 4. Probability Density Function 5. Expectation and Variance James Bond. I Escapes from SPECTRE sometime during 1 , 000 mile flight. I Uniformly likely to be at any point along path. James Bond. I Escapes from SPECTRE sometime during 1 , 000 mile flight. I Uniformly likely to be at any point along path. What is chance he is at any point along the path? James Bond. I Escapes from SPECTRE sometime during 1 , 000 mile flight. I Uniformly likely to be at any point along path. What is chance he is at any point along the path? Discrete Setting: Uniorm over = { 1 ,..., 1000 } . James Bond. I Escapes from SPECTRE sometime during 1 , 000 mile flight. I Uniformly likely to be at any point along path. What is chance he is at any point along the path? Discrete Setting: Uniorm over = { 1 ,..., 1000 } . Continuous setting: probability at any point in [ , 1000 ] ? Probability at any one of an infinite number of points is .. James Bond. I Escapes from SPECTRE sometime during 1 , 000 mile flight. I Uniformly likely to be at any point along path. What is chance he is at any point along the path? Discrete Setting: Uniorm over = { 1 ,..., 1000 } . Continuous setting: probability at any point in [ , 1000 ] ? Probability at any one of an infinite number of points is .. ...uh ... James Bond. I Escapes from SPECTRE sometime during 1 , 000 mile flight. I Uniformly likely to be at any point along path. What is chance he is at any point along the path? Discrete Setting: Uniorm over = { 1 ,..., 1000 } . Continuous setting: probability at any point in [ , 1000 ] ? Probability at any one of an infinite number of points is .. ...uh ...0? Continuous Probability: the interval! Consider [ a , b ] [ , ] (for James, = 1000 . ) Continuous Probability: the interval! Consider [ a , b ] [ , ] (for James, = 1000 . ) Let [ a , b ] also denote the event that point is in the interval [ a , b ] . Continuous Probability: the interval! Consider [ a , b ] [ , ] (for James, = 1000 . ) Let [ a , b ] also denote the event that point is in the interval [ a , b ] . Pr [[ a , b ]] = length of [ a , b ] length of [ , ] = b a = b a 1000 . Continuous Probability: the interval! Consider [ a , b ] [ , ] (for James, = 1000 . ) Let [ a , b ] also denote the event that point is in the interval [ a , b ] . Pr [[ a , b ]] = length of [ a , b ] length of [ , ] = b a = b a 1000 . Again, [ a , b ] = [ , ] are events. Continuous Probability: the interval!...
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 Fall '11
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