AP Stats Unit 6 Random Variables

What is the expected value of a random variable?

• The expected value is the maximum value of the random variable.

• The expected value is the long-term average of its possible values, weighted by their probabilities.

• The expected value is the most frequently occurring value in a dataset.

• The expected value is the difference between the highest and lowest values of a random variable.

What does it mean if a random variable has a standard deviation of 0.9?

• It means that the values of the random variable typically differ from the mean by about 0.9 units.

• It indicates that the random variable has a fixed value of 0.9.

• It suggests that the random variable is normally distributed with a mean of 0.9.

• It implies that the random variable has no variability at all.

What is the law of large numbers?

• The law of large numbers states that as the number of trials increases, the sample mean will converge to the expected value.

• The law of large numbers states that the sample mean will always equal the population mean regardless of the number of trials.

• The law of large numbers states that outcomes of random trials are independent of each other.

• The law of large numbers states that the variance of the sample mean decreases as the number of trials increases.

What is the standard deviation of a random variable?

• The standard deviation measures the dispersion or spread of a set of values around the mean.

• The standard deviation is the average of all values in a dataset.

• The standard deviation is a measure of the central tendency of a dataset.

• The standard deviation indicates the maximum value in a dataset.

What is a cumulative distribution function (CDF)?

• A function that describes the likelihood of a random variable taking on a specific value.

• A function that gives the probability that a random variable is less than or equal to a certain value.

• A function that represents the mean of a random variable.

• A function that shows the variance of a random variable.

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

• The probability of at least k successes is calculated by summing the probabilities of k, k+1, ..., n successes.

• The probability of at least k successes is calculated by multiplying the probabilities of k, k-1, ..., 0 successes.

• The probability of at least k successes is determined by the maximum probability of k successes only.

• The probability of at least k successes is found by averaging the probabilities of all possible outcomes.

What is the probability distribution of a discrete random variable?

• A probability distribution of a discrete random variable lists all possible values and their corresponding probabilities.

• A probability distribution of a discrete random variable is a graphical representation of the variable's outcomes.

• A probability distribution of a discrete random variable only includes the mean and variance of the outcomes.

• A probability distribution of a discrete random variable is a method to calculate the expected value.

How do you calculate the probability of getting a specific number of successes in a binomial experiment?

• P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

• P(X = k) = n * p * (1-p)^(n-k)

• P(X = k) = (n choose k) * p^(n-k) * (1-p)^k

• P(X = k) = (n + k) choose k * p^k * (1-p)^n

What is a probability mass function (PMF)?

• A function that defines the probability of a continuous random variable taking on a specific value.

• A probability mass function (PMF) defines the probability of a discrete random variable taking on a specific value.

• A method to calculate the mean of a random variable.

• A graphical representation of the distribution of a random variable.

How do you find the mean of a binomial distribution?

• The mean is calculated as n + p.

• The mean is calculated as n / p.

• The mean is calculated as n * p, where n is the number of trials and p is the probability of success.

• The mean is calculated as p / n.