AI Probability Distributions Flashcards
(26 cards)
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 can be discrete or continuous.
True
Fill in the blank: The sum of probabilities in a probability distribution must equal _____
1
What is the difference between a discrete probability distribution and a continuous probability distribution?
A discrete probability distribution deals with discrete outcomes, while a continuous probability distribution deals with continuous outcomes.
Name one example of a discrete probability distribution.
Binomial distribution
Name one example of a continuous probability distribution.
Normal distribution
What does the probability mass function (PMF) represent?
The PMF represents the probability that a discrete random variable is exactly equal to some value.
What does the probability density function (PDF) represent?
The PDF represents the probability that a continuous random variable falls within a particular range of values.
What is the expected value in a probability distribution?
The expected value is the long-term average or mean of a random variable’s possible values, weighted by their probabilities.
True or False: The variance measures the spread of a probability distribution.
True
What is the formula for calculating the variance of a discrete random variable?
Variance = Σ (xi - μ)² * P(xi), where μ is the expected value.
What is a cumulative distribution function (CDF)?
A CDF is a function that maps a value to the probability that a random variable is less than or equal to that value.
What type of distribution is characterized by a bell-shaped curve?
Normal distribution
Fill in the blank: In a normal distribution, approximately _____% of the data falls within one standard deviation of the mean.
68
What is the central limit theorem?
The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the original distribution.
True or False: The uniform distribution has equal probabilities for all outcomes.
True
What is a Poisson distribution typically used to model?
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space.
What is the key parameter of a binomial distribution?
The key parameters are the number of trials (n) and the probability of success (p).
What is the range of a probability distribution?
The range of a probability distribution is the set of all possible values that a random variable can take.
True or False: The total area under the curve of a probability density function equals 1.
True
What does it mean for two random variables to be independent?
Two random variables are independent if the occurrence of one does not affect the probability of the occurrence of the other.
What is skewness in a probability distribution?
Skewness measures the asymmetry of the probability distribution of a real-valued random variable.
Fill in the blank: A distribution is said to be _____ if it is skewed to the right.
positively skewed
What is a joint probability distribution?
A joint probability distribution describes the probability of two or more random variables occurring simultaneously.
