Discrete Random Variables

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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, often representing counts or categories.

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What is a probability distribution?

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A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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What are the conditions for a valid probability distribution?

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1. All probabilities must be between 0 and 1. 2. The sum of all probabilities must equal 1.

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What does it mean if the sum of p(x) does not equal 1?

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If the sum of p(x) does not equal 1, then the distribution is not a valid probability distribution.

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How do you find the value of k in a probability distribution?

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To find the value of k, set up the equation where the sum of all probabilities equals 1 and solve for k.

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What is the mean of a discrete random variable?

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The mean (expected value) of a discrete random variable is calculated by multiplying each possible value by its probability and summing the results.

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How do you calculate the standard deviation of a discrete random variable?

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Standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

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What is the variance of a discrete random variable?

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Variance is a measure of how much the values of a discrete random variable differ from the mean, calculated as the average of the squared differences.

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What is an example of a discrete random variable?

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An example of a discrete random variable is the number of heads when flipping a coin three times.

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What is the difference between a discrete and a continuous random variable?

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A discrete random variable can take on a countable number of values, while a continuous random variable can take on an infinite number of values within a given range.