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Uniform Distribution quiz

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  • What is the main difference between discrete and continuous random variables?
    Discrete random variables can only take specific, separate values, while continuous random variables can take any value within a range.
  • How are probabilities for discrete random variables typically represented?
    They are usually shown in a table or a graph with bars for each possible value.
  • Why can't we list all possible values for a continuous random variable in a table?
    Because there are infinitely many possible values within any range for a continuous random variable.
  • What is a probability density function (pdf)?
    A pdf is a function used to represent the probabilities of a continuous random variable over a range of values.
  • How do you find the probability that a continuous random variable falls within a certain interval?
    You calculate the area under the probability density function over that interval.
  • What is the total area under a probability density function for a continuous random variable?
    The total area is always 1, representing 100% probability.
  • How do you find the probability that a discrete random variable equals a specific value?
    You look up the probability assigned to that value in the table or graph.
  • What is the probability that a continuous random variable equals exactly a specific value?
    The probability is zero because there are infinitely many possible values.
  • Why is the probability that a continuous random variable equals a specific value zero?
    Because the probability is spread over an infinite number of possible values, making the probability for any single value effectively zero.
  • What is a uniform distribution?
    A uniform distribution is a continuous distribution where the probability density function has the same height for all values within its range.
  • How can you tell if a distribution is uniform by looking at its graph?
    If the probability density function has the same height for every possible value of x, it is a uniform distribution.
  • Is every continuous random variable uniformly distributed?
    No, the uniform distribution is a special case; not all continuous random variables have a uniform distribution.
  • How do you calculate the probability that x is between two values in a uniform distribution?
    Multiply the constant height of the pdf by the width of the interval between the two values.
  • What does the height of the probability density function represent in a uniform distribution?
    It represents the constant probability density for all values within the range.
  • If the range of a uniform distribution is from 0 to 6, what is the height of the pdf?
    The height is 1 divided by the width of the range, so 1/6.