Cheat Sheet
5 sections
•
21 key points
1
Basic Probability Rules
P(A) = (Number of favorable outcomes) / (Total number of outcomes).
0 ≤ P(A) ≤ 1 for any event A.
P(A') = 1 - P(A) (Complement Rule).
P(A U B) = P(A) + P(B) - P(A ∩ B) (Addition Rule).
P(A ∩ B) = P(A) * P(B|A) (Multiplication Rule).
2
Bayes' Theorem
P(A|B) = [P(B|A) * P(A)] / P(B).
Used to update the probability of a hypothesis (A) given new evidence (B).
P(A|B) is the posterior probability.
P(A) is the prior probability, P(B|A) is the likelihood.
3
Normal Distribution
Bell-shaped, symmetrical, unimodal distribution.
Defined by its mean (μ) and standard deviation (σ).
Empirical Rule (68-95-99.7 rule): percentages of data within 1, 2, and 3 std devs from mean.
Many natural phenomena follow a normal distribution.
4
Binomial Distribution
Describes the number of successes in a fixed number of independent Bernoulli trials.
Conditions: Fixed number of trials (n), two possible outcomes (success/failure), independent trials, constant probability of success (p).
PMF: P(X=k) = C(n, k) * p^k * (1-p)^(n-k).
Mean = np, Variance = np(1-p).
5
Hypothesis Testing & Confidence Intervals
Hypothesis Testing: Formal procedure to evaluate claims about populations using sample data.
Null Hypothesis (H0) vs. Alternative Hypothesis (H1).
P-value: The probability of observing data as extreme as, or more extreme than, what was observed, assuming H0 is true.
Confidence Interval: A range of values that is likely to contain the true population parameter with a certain level of confidence (e.g., 95%).
Sample Flashcards
Card 1 of 6
Question
What is the range of possible values for a probability?
Answer
0 to 1 (inclusive)
Click the card to flip
Quick Quiz
1. If the probability of event A is 0.4 and the probability of event B is 0.5, and A and B are independent, what is the probability of both A and B occurring?
2. Which of the following distributions is characterized by a bell-shaped, symmetrical curve?
3. In a hypothesis test, if the p-value is less than the significance level (alpha), what is the typical conclusion?
4. Bayes' Theorem is particularly useful for:
5. A binomial distribution applies to situations where there are:
Frequently Asked Questions
What is the basic definition of probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means it is certain.
What is the key difference between a discrete and continuous probability distribution?
A discrete probability distribution describes the probabilities of events that can be counted (e.g., number of heads in coin flips), while a continuous probability distribution describes probabilities for variables that can take any value within a range (e.g., height, temperature).
What is the purpose of a hypothesis test?
A hypothesis test is a statistical method used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for an entire population. It involves setting up null and alternative hypotheses and analyzing data to make a decision.
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