Flashcard--Discrete and Random Variables

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What is a discrete random variable?

Back

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 heads when flipping a coin multiple times.

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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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Define 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 is the probability of getting exactly k successes in n independent Bernoulli trials?

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The probability is given by the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success on an individual trial.

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What does P(X > 2) represent?

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P(X > 2) represents the probability that the random variable X takes on a value greater than 2.

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How do you calculate the probability of at least k successes?

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To calculate the probability of at least k successes, sum the probabilities of getting k, k+1, ..., up to n successes.

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What is the expected value of a discrete random variable?

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The expected value is the long-term average value of repetitions of the experiment it represents, calculated as E(X) = Σ [x * P(X = x)] for all possible values x.

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What is the variance of a discrete random variable?

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Variance measures the spread of a set of values and is calculated as Var(X) = E(X^2) - (E(X))^2.

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What is the difference between discrete and continuous random variables?

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Discrete random variables take on countable values, while continuous random 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 cars sold by a dealership in a month.