Probability Distributions Flashcards
What is a probability distribution?
A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
True or False: A probability distribution must sum to 1.
True
What is the difference between discrete and continuous probability distributions?
Discrete probability distributions deal with countable outcomes, while continuous probability distributions deal with outcomes that can take any value within a given range.
Fill in the blank: The ______ distribution is commonly used to model the number of successes in a fixed number of independent Bernoulli trials.
binomial
What is the expectation (mean) of a discrete random variable?
The expectation of a discrete random variable is the weighted average of all possible values, where the weights are the probabilities of each value.
What does the standard deviation measure in a probability distribution?
The standard deviation measures the amount of variation or dispersion of a set of values in a probability distribution.
Which distribution is used to model the time until an event occurs?
The exponential distribution.
True or False: The normal distribution is symmetric around its mean.
True
What is the shape of a Poisson distribution?
The Poisson distribution is typically skewed to the right, especially for small mean values.
Fill in the blank: A ______ distribution describes the probability of a given number of events happening in a fixed interval of time or space.
Poisson
What is the cumulative distribution function (CDF)?
The 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.
What are the parameters of a normal distribution?
The parameters of a normal distribution are the mean (μ) and the standard deviation (σ).
True or False: A uniform distribution has equal probabilities for all outcomes.
True
What is a characteristic of the binomial distribution?
The binomial distribution is characterized by two parameters: the number of trials (n) and the probability of success (p) in each trial.
Fill in the blank: In a normal distribution, approximately ______% of the data falls within one standard deviation of the mean.
68
What is the variance of a random variable?
The variance is a measure of the spread of a probability distribution and is the average of the squared deviations from the mean.
Which distribution is often used to model binary outcomes?
The Bernoulli distribution.
True or False: The area under the probability density function of a continuous random variable equals 1.
True
What is the purpose of the Central Limit Theorem?
The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the original distribution.
What is the probability mass function (PMF)?
The probability mass function (PMF) gives the probability that a discrete random variable is exactly equal to some value.
Fill in the blank: The ______ distribution is used to model the number of events that occur in a fixed interval of time or space.
Poisson
What is a characteristic of the geometric distribution?
The geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials.
Which distribution is symmetric and bell-shaped?
The normal distribution.
True or False: A negative binomial distribution models the number of trials until a specified number of successes occurs.
True
What is the range of a probability distribution?
The range of a probability distribution is the set of all possible values that the random variable can take.
What does it mean if a distribution is skewed?
A skewed distribution has a longer tail on one side than the other, indicating that the data is not symmetrically distributed.
