text: # Mean of a discrete random variable
  
  The mean of a discrete random variable x is the average value that we would expect to get if the experiment is repeated a large number of times.
  
  The mean is denoted by μ and obtained using the formula μ = ΣxP(x)
  
  Another name for the mean of a discrete random variable is expected value.
  
  The expected value is denoted by E(x), so E(x) = ΣxP(x)
  
  In the lesson about probability distribution of a discrete random variable, we have the probability distribution table below. Use it to compute the mean number of vehicles owned by people.
  
   Number of vehicles owned or x Probability or P(x) 0 0.2 1 0.5 2 0.3 ΣP(x) = 1
  
  Here is how to calculate the mean for the probability distribution of number of vehicles owned by people.
  
   x P(x) xP(x) = x × P(x) 0 0.2 0 × 0.2 = 0 1 0.5 1 × 0.5 = 0.5 2 0.3 2 × 0.3 = 0.6 ΣxP(x) = 0 + 0.5 + 0.6 = 1.1
  
  E(x) = 1.1
  
  What does an expected value of 1.1 mean for this situation? It means that on average, you would expect people to own about 1.1 vehicles.
  
  ## Another example showing how to find the mean of a discrete random variable
  
  A survey was conducted to find out how many times people go to the movie theater per week. After interviewing 500 people, the result is shown in the table below. Let x be the number of times people go to the movie theater per week. When x  = 2, the frequency is 75. This means that 75 people went to the movie theater twice per week.
  
   x Frequency 0 250 1 125 2 75 3 45 4 5 N = 500
  
  P(x = 0) = 250/500 = 0.5
  P(x = 1) = 125/500 = 0.25
  P(x = 2) = 75/500 = 0.15
  p(x = 3) = 45/500 = 0.09
  P(x = 4) = 5/500 = 0.01
  
  The table below shows the probability distribution.
  
   x P(x) 0 0.5 1 0.25 2 0.15 3 0.09 4 0.01 ΣP(x) = 1
  
  Here is how to calculate the mean for the probability distribution of number of times people go to the movie theater.
  
  E(x) =  ΣxP(x) = 0 × 0.5 + 1 × 0.25 + 2 × 0.15 + 3 × 0.09 + 4 × 0.01
  
  E(x) = 0 + 0.25 + 0.30 + 0.27 + 0.04
  
  E(x) = 0.86
  
  Based on the expected value of 0.86, the mean number of times people will go to the movie theater per week is 0.86.
  
  100 Tough Algebra Word Problems.
  
  If you can solve these problems with no help, you must be a genius!
  
  Recommended
explanation: The document provides an explanation of the mean of a discrete random variable, including its formula and alternative names. It includes two examples with detailed calculations to find the mean (expected value) of the number of vehicles owned and the number of times people go to the movie theater per week. Each example includes a probability distribution table and the step-by-step calculation of the expected value. The document also interprets the meaning of the expected values in the context of the examples.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Mean of a discrete random variable
  
  The mean of a discrete random variable x is the average value that we would expect to get if the experiment is repeated a large number of times.
  
  The mean is denoted by μ and obtained using the formula μ = ΣxP(x)
  
  Another name for the mean of a discrete random variable is expected value.
  
  The expected value is denoted by E(x), so E(x) = ΣxP(x)
  
  In the lesson about probability distribution of a discrete random variable, we have the probability distribution table below. Use it to compute the mean number of vehicles owned by people.
  
   Number of vehicles owned or x Probability or P(x) 0 0.2 1 0.5 2 0.3 ΣP(x) = 1
  
  Here is how to calculate the mean for the probability distribution of number of vehicles owned by people.
  
   x P(x) xP(x) = x × P(x) 0 0.2 0 × 0.2 = 0 1 0.5 1 × 0.5 = 0.5 2 0.3 2 × 0.3 = 0.6 ΣxP(x) = 0 + 0.5 + 0.6 = 1.1
  
  E(x) = 1.1
  
  What does an expected value of 1.1 mean for this situation? It means that on average, you would expect people to own about 1.1 vehicles.
  
  ## Another example showing how to find the mean of a discrete random variable
  
  A survey was conducted to find out how many times people go to the movie theater per week. After interviewing 500 people, the result is shown in the table below. Let x be the number of times people go to the movie theater per week. When x  = 2, the frequency is 75. This means that 75 people went to the movie theater twice per week.
  
   x Frequency 0 250 1 125 2 75 3 45 4 5 N = 500
  
  P(x = 0) = 250/500 = 0.5
  P(x = 1) = 125/500 = 0.25
  P(x = 2) = 75/500 = 0.15
  p(x = 3) = 45/500 = 0.09
  P(x = 4) = 5/500 = 0.01
  
  The table below shows the probability distribution.
  
   x P(x) 0 0.5 1 0.25 2 0.15 3 0.09 4 0.01 ΣP(x) = 1
  
  Here is how to calculate the mean for the probability distribution of number of times people go to the movie theater.
  
  E(x) =  ΣxP(x) = 0 × 0.5 + 1 × 0.25 + 2 × 0.15 + 3 × 0.09 + 4 × 0.01
  
  E(x) = 0 + 0.25 + 0.30 + 0.27 + 0.04
  
  E(x) = 0.86
  
  Based on the expected value of 0.86, the mean number of times people will go to the movie theater per week is 0.86.
  
  100 Tough Algebra Word Problems.
  
  If you can solve these problems with no help, you must be a genius!
  
  Recommended
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides an explanation of the mean of a discrete random variable, including its formula and alternative names. It includes two examples with detailed calculations to find the mean (expected value) of the number of vehicles owned and the number of times people go to the movie theater per week. Each example includes a probability distribution table and the step-by-step calculation of the expected value. The document also interprets the meaning of the expected values in the context of the examples.
  
  Label: question-and-answer