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general addition rule

⭐ General Addition Rule The general addition rule tells you how to find the probability that A or B happens — even when the events overlap. 📌 The formula Why subtract the intersection?Because if A… general addition rule

Independent event

⭐ Independent Events Two events are independent when one happening does not change the probability of the other. That’s the whole heart of it. 📌 Formal definition Events and are independent if This equation is… Independent event

Complementary events

⭐ Complementary Events Two events are complements when they cover the entire sample space together and cannot happen at the same time. If is an event, then its complement is: 📌 Key properties 🎯 Examples… Complementary events

Sample and Event

⭐ Sample vs. Event Think of probability as a story with two levels: 🎯 Sample Space (S) The sample space is the complete list of everything that could happen in an experiment. Examples Key idea… Sample and Event

Random Variable

Random variables are essential components in probability theory and statistics, serving as numerical outcomes of random phenomena. Understanding the behavior of random variables allows practitioners to make informed decisions about the likely outcomes of complex… Random Variable

Classical definite of Probability

The classical probability definition calculates the likelihood of an event based on favorable and total outcomes, illustrated with examples.

normal distribution comics & song

This song helps us better remember the properties of the normal distribution. A normal distribution, also known as a Gaussian distribution, is a symmetrical, bell-shaped continuous probability distribution characterized by its mean (?) and standard deviation (?). It exhibits properties such as symmetry, unimodality, and follows the 68-95-99.7 rule, indicating the distribution of data within standard deviations of the mean.

Poisson Distribution

Quizzes Question: In the context of economics, what is the primary characteristic of events that makes them suitable for modeling with a Poisson distribution?A) Events are dependent on each otherB) Events occur at a constant… Poisson Distribution

Bernoulli distribution

Quizzes In an economic context, a Bernoulli distribution can be used to model:a. The distribution of income across a populationb. The probability of a consumer making a purchase or notc. The stock market index changesd.… Bernoulli distribution

quizzes: covariance

Question: What does a covariance of zero between two random variables and indicate?A) and are independent.B) and are uncorrelated.C) and are dependent.D) and have the same variance. Question: If , what does this indicate about… quizzes: covariance

Quizzes: variance

Question: What is the variance of a fair six-sided die roll?A) 2.5B) 3.5C) 2.9167D) 1.5 Question: If is a random variable with variance , what is ?A) 4B) 8C) 16D) 2 Answer: C) 16 Question:… Quizzes: variance

Quizzes: expectation

Question: What is the expected value of a fair six-sided die roll?A) 2.5B) 3.5C) 4.5D) 5.5 Question: If is a random variable with expected value , what is ?A) 2B) 4C) 6D) 8 Question: What… Quizzes: expectation

Uniform distribution

The Uniform Distribution is a type of probability distribution in which all outcomes are equally likely. It’s a continuous distribution, meaning that it takes on an uncountable number of possible values. For any given interval… Uniform distribution

independent events

Quizzes Question: If the probability of using Facebook is 0.6 and the probability of using Instagram is 0.5, and these events are independent, what is the probability of using both Facebook and Instagram?Options:A) 0.3B) 0.9C)… independent events

Combinations

A combination is a selection of items from a larger set, where the order of selection does not matter. For example, suppose you have a set of three different fruits: Apple (A), Banana (B), and… Combinations

product rule & quizzes

Quizzes about the product rule Question: An engineer has 4 different types of screws and 3 different types of bolts. How many different combinations of screws and bolts can the engineer choose from?a) 7b) 12c)… product rule & quizzes

s-Permutation

Example: password generation. Suppose you are generating a password using the characters A, B, and C. The password must be 3 characters long, and each character can be used once. Here, the S-permutation will be… s-Permutation

Exponential distribution

This song helps us better remember the properties of the exponential distribution. The exponential distribution models time between events in a Poisson process, where occurrences are independent at a constant rate. Key features include its probability density and cumulative distribution functions, mean, variance, and memoryless property. It has applications in queueing theory, reliability engineering, and survival analysis.

The success rates of Cupid’s arrows

I advised a master’s student to use the binomial probability formula to determine the likelihood of attracting the affection of 15 girls, with Cupid’s success rate at 0.7. The analysis shows that the highest probability of success occurs when 10 girls reciprocate love, with a probability of 0.33.

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