Module 7 Practice Questions

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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 defective items in a batch.

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What is a continuous random variable?

Back

A continuous random variable is a variable that can take on an infinite number of values within a given range. Examples include height, weight, and temperature.

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What is the mean of a probability distribution?

Back

The mean of a probability distribution is the average of all possible values of the random variable, weighted by their probabilities. It represents the expected value.

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How do you calculate the probability of at least 'k' successes in a binomial distribution?

Back

To calculate the probability of at least 'k' successes, sum the probabilities of getting 'k' or more successes using the binomial probability formula.

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What is the probability distribution?

Back

A probability distribution describes how the probabilities are distributed over the values of the random variable. It can be discrete or continuous.

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What is the difference between a random variable and a probability distribution?

Back

A random variable is a variable whose values are determined by the outcomes of a random phenomenon, while a probability distribution describes the likelihood of each possible value of that random variable.

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What does it mean for a random variable to be independent?

Back

Two random variables are independent if the occurrence of one does not affect the probability of the occurrence of the other.

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What is the significance of the standard deviation in a probability distribution?

Back

The standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean.

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What is a probability mass function (PMF)?

Back

A probability mass function (PMF) is a function that gives the probability that a discrete random variable is equal to a specific value.

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What is a cumulative distribution function (CDF)?

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A cumulative distribution function (CDF) is a function that describes the probability that a random variable takes on a value less than or equal to a specific value.