Discrete Random Variables: Section 5 Notes

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Questions and Answers

What is the main distinction between a variable and a random variable?

  • A variable depends on chance, while a random variable does not.
  • A random variable maps the sample space to real numbers, while a variable does not. (correct)
  • A random variable describes the likelihood of quantitative outcomes across an entire population, while a variable does not.
  • A variable is a statistical concept, while a random variable is not.

How are random variables typically denoted?

  • With symbols from the middle of the alphabet
  • With lowercase letters
  • With symbols from the beginning of the alphabet (correct)
  • With numbers

Why is it crucial to correctly identify a quantitative variable as either discrete or continuous?

  • To find probabilities in the same way for both types
  • To distinguish how probabilities are calculated for discrete and continuous random variables (correct)
  • To assign values to each possible outcome
  • To determine its sample space

Which of the following is NOT true regarding random variables?

<p>Random variables are always denoted by lowercase letters. (A)</p>
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In what context are random variables and populations often used together?

<p>In statistics (C)</p>
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What is a discrete random variable?

<p>A variable with a finite number of outcomes in the sample space (B)</p>
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What is a common characteristic of a discrete random variable?

<p>Outcomes can be represented in a list (D)</p>
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Which criteria must be met for a discrete random variable to exist?

<p>Sum of all probabilities for individual outcomes must be equal to 1 (D)</p>
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What does the expected value of a random variable represent?

<p>The mean of the variable weighted by probabilities (A)</p>
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How is the expected value of a general discrete random variable calculated?

<p>$E(X) = \Sigma x_i \times P(X = x_i)$ (A)</p>
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