Statistics and Probability: Computing Mean, Variance, Standard Deviation
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Questions and Answers

What is the formula to calculate the standard deviation of a probability distribution?

  • √∑(𝑿 − 𝝁)𝟐
  • √∑(𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿) (correct)
  • √∑(𝑿 − 𝝁)𝟐 / 𝑷(𝑿)
  • ∑(𝑿 − 𝝁)𝟐

    • What is the purpose of Step 3 in finding the mean, variance, and standard deviation of a probability distribution?

  • Find the mean (correct)
  • Find the square root of the variance
  • Subtract the computed mean from each value of random variable
  • Square the result

    • In Step 4 of the process, what does 𝝁 represent?

  • Computed mean (correct)
  • Standard deviation
  • Random variable
  • Variance

    • What is the purpose of Step 8 in the process of finding the standard deviation?

    <p>Find the square root of the variance</p> Signup and view all the answers

    To calculate the standard deviation, what needs to be done in Step 6 of the process?

    <p>(𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿)</p> Signup and view all the answers

    What does the standard deviation of a random variable measure?

    <p>The distance between the random variable and the mean</p> Signup and view all the answers

    What is the formula for the standard deviation of a discrete probability distribution?

    <p>$\sqrt{\sum (X - \mu)^2 \cdot P(X)}$</p> Signup and view all the answers

    What is the next step after multiplying each value of X by its corresponding probability value in finding the standard deviation?

    <p>Find the mean of the expected value</p> Signup and view all the answers

    How is the variance calculated in the context of a probability distribution?

    <p>$\sum (X - \mu)^2 \cdot P(X)$</p> Signup and view all the answers

    What is the purpose of squaring $(X-\mu)$ in finding the standard deviation?

    <p>To get positive values</p> Signup and view all the answers

    What does it mean if the variance of a probability distribution is zero?

    <p>All values in the distribution are identical</p> Signup and view all the answers

    What is the formula for computing the mean of a discrete probability distribution?

    <p>𝝁 = ∑ 𝑿 ∙ 𝑷(𝑿)</p> Signup and view all the answers

    What does the variance of a discrete random variable measure?

    <p>Spread or Variability</p> Signup and view all the answers

    In finding the mean of a discrete probability distribution, what do you do after constructing the probability distribution?

    <p>Determine the value of 𝑿 ∙ 𝑷(𝑿)</p> Signup and view all the answers

    What should you do first when finding the variance of a discrete probability distribution?

    <p>Subtract the computed mean from each value</p> Signup and view all the answers

    How is the variance calculated in a discrete probability distribution?

    <p>(𝑿 − 𝝁)𝟐</p> Signup and view all the answers

    Which step is crucial in determining the spread of a discrete random variable's distribution?

    <p>(𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿)</p> Signup and view all the answers

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