Continuous and rest till anova (p-values) Flashcards
What is the Normal Distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution frequently encountered in nature. It is defined by its mean and standard deviation and forms a characteristic bell-shaped curve. Example: IQ scores in a population often follow a normal distribution. For instance, if the mean IQ score is 100 and the standard deviation is 15, the distribution captures the variation in IQ scores.
What is the Uniform Distribution?
The uniform distribution assigns equal probabilities to all outcomes within a specified interval. It models situations where each outcome has the same likelihood. Example: Rolling a fair six-sided die illustrates a uniform distribution, where each number (1 to 6) has an equal probability of 61. |
What is the Exponential Distribution?
The exponential distribution models the time between events in a Poisson process. It is often used for modeling waiting times or lifetimes and possesses a memoryless property. Example: Consider the time between arrivals of customers at a fast-food drive-thru with an average arrival rate of 3 minutes. The exponential distribution can model the time between successive arrivals. |
What is the Gamma Distribution?
The gamma distribution is a versatile distribution used to model various types of continuous random variables. It encompasses the exponential distribution as a special case. Example: To model the time it takes for a machine to produce a certain number of parts, the gamma distribution can be employed. If the machine produces an average of 100 parts per hour, the distribution captures production times. |
What is the Beta Distribution?
The beta distribution models probabilities or proportions and exhibits diverse shapes. It is commonly used in Bayesian analysis and quality control. Example: In a clinical trial, the proportion of patients responding positively to a new drug can be represented using a beta distribution, aiding in estimating a range of possible response rates. |
What is the Chi-Square Distribution?
The chi-square distribution is commonly used in statistical hypothesis testing and arises when summing the squares of independent standard normal random variables. Example: When testing the independence of two categorical variables, such as smoking habits and lung cancer incidence, the chi-square distribution is utilized to assess the significance of the association. |
What is the Student’s t-Distribution?
The t-distribution is employed when estimating the mean of a normally distributed population from a small sample or when the population standard deviation is unknown. Example: Suppose you wish to estimate the average time spent on a task from a small sample of 12 observations. The t-distribution is used to construct a confidence interval for the population mean. |
What is the Log-Normal Distribution?
The log-normal distribution models data that are positively skewed and cannot take negative values. It is often used in financial modeling and describes multiplicative growth. Example: The distribution of housing prices in a city can often be described using a log-normal distribution, accounting for positive skewness and preventing negative prices. |
What is the Weibull Distribution?
The Weibull distribution models the distribution of lifetimes or failure times of objects. It can take different shapes to describe various failure patterns. Example: The lifetime of electronic components, such as light bulbs, can be modeled using a Weibull distribution. Different shapes of the distribution correspond to different failure patterns. |
What is the Cauchy Distribution?
The Cauchy distribution is characterized by its heavy tails and lack of finite moments. It is used to describe certain types of distributions in physics, engineering, and other fields. Example: In a physics experiment involving interference patterns, the distribution of phase differences between waves can be modeled using a Cauchy distribution. |
What is the Pareto Distribution?
The Pareto distribution is used to model distributions where a small number of observations account for the majority of occurrences. It is often used in economics and finance. Example: In economics, the distribution of income or wealth often follows a Pareto distribution, where a small percentage of individuals hold the majority of resources. |
What is the Exponential Power Distribution?
The exponential power distribution is a flexible distribution capable of modeling a wide range of shapes and tail behaviors. It is used in economics, finance, and engineering to handle diverse datasets. Example: The distribution of rainfall intensity during heavy storms can be modeled using an exponential power distribution to capture different patterns of intensity variation. |
What is Bayes’ Theorem, and how does it relate to machine learning?
Bayes’ Theorem is a fundamental concept in probability theory and statistics. It provides a way to update predictions based on new evidence. In machine learning, it’s used for classification tasks like spam detection or medical diagnosis.
Can you provide an example of Bayes’ Theorem in spam email detection?
Certainly! Consider a scenario where you’re building a spam filter. Given prior probabilities and keyword occurrence probabilities, Bayes’ Theorem helps calculate the chance an email is spam based on keywords.
How does Bayes’ Theorem enhance decision-making in machine learning?
Bayes’ Theorem improves decision-making by incorporating prior knowledge and new evidence. It adjusts probabilities to update beliefs, leading to more accurate classifications and informed decisions.
What is Prior Probability (Prior)?
Prior Probability: The initial belief or probability of an event occurring before considering new evidence.Example: In a medical test for a rare disease, the prior probability of a person having the disease might be 0.001 (0.1%).
What is Posterior Probability (Posterior)?
Posterior Probability: The updated probability of an event occurring after considering new evidence using Bayes’ Theorem.Example: After a positive test result, the posterior probability of a person having the disease is recalculated based on the test.
What is Likelihood?
Likelihood: The probability of observing the evidence (data) given a specific hypothesis or event.Example: In a coin flip, the likelihood of getting heads given that the coin is fair is 0.5.
What is Evidence (Data)?
Evidence (Data): The observed information that is used to update probabilities.Example: In spam email detection, the evidence could be the presence of specific keywords in an email.
What is Marginal Probability?
Marginal Probability: The probability of a single event occurring, disregarding any other events.Example: The probability of rolling a 4 on a fair six-sided die is a marginal probability.
What is Conditional Probability?
Conditional Probability: The probability of one event occurring given that another event has already occurred.Example: The probability of a patient having a disease given that they exhibit certain symptoms.
What is Joint Probability?
Joint Probability: The probability of two or more events occurring together.Example: The joint probability of rolling a 3 and flipping a head on two independent coin tosses.
What is Law of Total Probability?
Law of Total Probability: A formula that computes the probability of an event by considering all possible ways it can occur.Example: Calculating the probability of a student passing a course by considering the probability of passing given study time.
What is Bayes’ Factor?
Bayes’ Factor: A measure of the strength of evidence for one hypothesis compared to another, obtained by a ratio.Example: Comparing the hypothesis that a medical treatment is effective versus the hypothesis that it is not based on patient outcomes.