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Lecture 2 Capture

# Lecture 2 Capture - EEL 5544 Lecture 2 EEL 5544 Lecture 2...

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EEL 5544 Lecture 2

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EEL 5544 Lecture 2 EX Motivation problem from Lecture 1A: An elementary school is offering 3 language classes: one in Spanish ( S ), one in French ( F ), and one in German ( G ). These classes are open to any of the 100 students in the school ( Ω ). There are 28 students in the S , 26 in F , and 16 in G . There are 12 students that are in both S and F , 4 that are in both S and G , and 6 that are in both F and G . (Note that being in “both S and G ” does not exclude that some of those students could also be in French.) In addition, there are 2 students taking all 3 classes. EEL 5544 L2-1
1. If a student is chosen randomly, what is the probability that he or she is not in any of these classes? Hint: Find the number of students that are not in any of these classes and divide by the total number of students. EEL 5544 L2-2

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EEL 5544 L2-3
2. If a student is chosen randomly, what is the probability that he or she is taking exactly one language class? Hint: Find the number of students that are in exactly one language class and divide by the total number of students. EEL 5544 L2-4

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Probability as a Measure of Frequency of Occurrence
Probability as a Measure of Frequency of Occurrence Consider a random experiment that has K possible outcomes, K <

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Probability as a Measure of Frequency of Occurrence Consider a random experiment that has K possible outcomes, K < Let N k ( n ) = the number of times the outcome is k
Probability as a Measure of Frequency of Occurrence Consider a random experiment that has K possible outcomes, K < Let N k ( n ) = the number of times the outcome is k Then we can tabulate N k ( n ) for various values of k and n

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Probability as a Measure of Frequency of Occurrence Consider a random experiment that has K possible outcomes, K < Let N k ( n ) = the number of times the outcome is k Then we can tabulate N k ( n ) for various values of k and n We can reduce the dependence on n by dividing N ( k ) by n to find out “how often did k occur”. EEL 5544 L2-5
The relative frequency

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The relative frequency of outcome k of a random experiment is f k ( n ) = N k ( n ) n .
The relative frequency of outcome k of a random experiment is f k ( n ) = N k ( n ) n . Observation: In our previous experiments, as n gets large, f k ( n ) converges to some constant value. EEL 5544 L2-6

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An experiment possesses statistical regularity
An experiment possesses statistical regularity if lim n f k ( n ) = p k (a constant) , k .

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An experiment possesses statistical regularity if lim n f k ( n ) = p k (a constant) , k . For experiments with statistical regularity as defined above, p k is called the probability of outcome k . EEL 5544 L2-7
P ROPERTIES OF R ELATIVE F REQUENCY

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P ROPERTIES OF R ELATIVE F REQUENCY Note that 0 N k ( n ) n , k
P ROPERTIES OF R ELATIVE F REQUENCY Note that 0 N k ( n ) n , k because N k ( n ) is just the # of times outcome k occurs in n trials.

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P ROPERTIES OF R ELATIVE F REQUENCY Note that 0 N k ( n ) n , k because N k ( n ) is just the # of times outcome k occurs in n trials.
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Lecture 2 Capture - EEL 5544 Lecture 2 EEL 5544 Lecture 2...

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