Understanding Developing a Probability Distribution from Empirical Data
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Beginner
Start here! Easy to understand
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Beginner Explanation
To build an empirical probability distribution, list each outcome x_i and compute P(x_i)=frequency of x_i / total frequencies. For example, if 3 movies occur 34 times out of 100, then P(3)=$34/100=0.34$.
Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
Consider the following empirical data on number of movies watched per student in one month: Outcome x_i: 1, 2, 3, 4, 5 Frequencies (percent): 10%, 20%, 34%, 18%, 18% What is the probability that a randomly selected student watches 3 movies in a month?
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
A survey of 120 high school students records the number of movies watched last month as follows: 0 movies: 24; 1 movie: 36; 2 movies: 30; 3 movies: 18; 4 movies: 12. Using this empirical data, calculate the expected number of movies watched.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Analyze the following data of movie-watching frequencies per week among adults: Outcome x_i: 0, 1, 2, 3 Frequencies (out of 100 observations): 5, 15, 50, 30 Construct the empirical distribution and calculate the expected value.
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4
Challenge Quiz
Single Choice Quiz
Advanced
Given a complex data set, how would you calculate the expected number of movies watched? $E(x) = \sum x_i \cdot P(x_i)$
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