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Discrete Random Variables quiz

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  • What is a random variable in probability?
    A random variable is a variable that represents a single number determined by chance for each outcome of an experiment.
  • How are discrete random variables different from continuous random variables?
    Discrete random variables have distinct, countable outcomes, while continuous random variables can take any value within a range.
  • What is a classic example of a discrete random variable?
    A dice roll is a classic example, with outcomes of 1, 2, 3, 4, 5, or 6.
  • What is a probability distribution?
    A probability distribution is a table showing the probabilities of all possible values that a random variable can take.
  • What are the two criteria for a probability distribution?
    All probabilities must be between 0 and 1, and the sum of all probabilities must equal 1.
  • How do you find a missing probability in a probability distribution table?
    Subtract the sum of the known probabilities from 1 to find the missing probability.
  • What does 'at least' mean when calculating probabilities?
    'At least' means you add up the probabilities for all outcomes that meet or exceed the specified value.
  • How do you calculate the mean of a discrete random variable?
    Multiply each outcome by its probability, then sum these products to get the mean.
  • What is the equation for the mean of a discrete random variable?
    The mean is calculated as μ = Σxi·P(xi), where xi is an outcome and P(xi) is its probability.
  • What does 'expected value' mean in probability distributions?
    Expected value is another term for the mean of a probability distribution.
  • Why can't you just average the outcomes in a probability distribution?
    Because each outcome has a different probability, so you must weight them accordingly.
  • How do you interpret the mean of a discrete random variable if it is not one of the possible outcomes?
    It represents the average outcome over many trials, even if it is not a possible single outcome.
  • What does variance measure in a probability distribution?
    Variance measures how spread out the outcomes of the experiment are.
  • How do you calculate variance for a discrete random variable?
    Sum the products of each squared outcome and its probability, then subtract the square of the mean.
  • How is standard deviation related to variance in probability distributions?
    Standard deviation is the square root of the variance.