Statistics 6.1 Random Variables & Probability Distributions

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What is a probability distribution?

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A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take. It must satisfy two conditions: all probabilities must be between 0 and 1 inclusive, and the sum of all probabilities must equal 1.

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What is a discrete random variable?

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A discrete random variable is a type of variable that can take on a countable number of distinct values. Examples include the number of students in a class or the number of cheeseburgers sold in a day.

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What is a continuous random variable?

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A continuous random variable is a variable that can take on an infinite number of values within a given range. Examples include the height of students or the time it takes to run a race.

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What is a random variable?

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A random variable is a variable whose values depend on the outcomes of a random phenomenon. It can be either discrete or continuous.

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How do you determine if a set of probabilities forms a probability distribution?

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To determine if a set of probabilities forms a probability distribution, check that each probability is between 0 and 1 inclusive, and that the sum of all probabilities equals 1.

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What is the difference between discrete and continuous variables?

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Discrete variables can take on specific, countable values, while continuous variables can take on any value within a range.

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Provide an example of a discrete random variable.

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An example of a discrete random variable is the number of tornadoes in a month.

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Provide an example of a continuous random variable.

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An example of a continuous random variable is the amount of rainfall in a month.

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What is the probability of an event?

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The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 (impossible event) and 1 (certain event).

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What does it mean for a distribution to be symmetric?

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A symmetric distribution is one where the left side of the distribution is a mirror image of the right side, meaning the probabilities are evenly distributed around the mean.