Basic probability rules with examples . Row-reduce A. 72 0 obj >> endobj >> AP Statistics Study Sheet: Discrete Probability Distributions Answers Page 1 of 5 These exercises focus on discrete probability distributions and random variables. endobj 37 0 obj << /S /GoTo /D (section.2.4) >> << /S /GoTo /D (section.1.2) >> Nathan Ferguson. << /S /GoTo /D (subsection.1.1) >> 56 0 obj By noting $f_X$ and $f_Y$ the distribution function of $X$ and $Y$ respectively, we have: Leibniz integral rule Let $g$ be a function of $x$ and potentially $c$, and $a, b$ boundaries that may depend on $c$. The complement of a set consists of all possible outcomes outside of the set. 53 0 obj endobj Students can add it to their interactive notebooks and is a great way for them to organize information. endobj Grades: Dummies helps everyone be more knowledgeable and confident in applying what they know. endobj endobj JFIF H H ;CREATOR: gd-jpeg v1.0 (using IJG JPEG v62), quality = 90 However, cloudy mornings are common; about 40% of days start off cloudy. 76 0 obj . The statisti-cian makes a guess (prior distribution) and then updates that guess with the data. 80 0 obj endobj Complete Stories by Rudy Rucker . math, discrete, induction, eecs, 203 and 6 more . Her particular research interests are curriculum materials development, teacher training and support, and immersive learning environments. We have: Chebyshev's inequality Let $X$ be a random variable with expected value $\mu$. That is, an event is a set consisting of possible outcomes of the experiment. Probability Distribution are in a way modeling of our real world. Similarly throwing a dice, where we have 6 values for a random variable and so Binomial . Dr. Rumsey has served on the American Statistical Associations Statistics Education Executive Committee and is the Editor of the Teaching Bits section of the Journal of Statistics Education. Shes the author of the books Statistics For Dummies and Statistics Workbook For Dummies (Wiley). It is computed as follows: Remark: the $k^{th}$ moment is a particular case of the previous definition with $g:X\mapsto X^k$. What is the Probability Density Function (PDF)? High School Teachers - you're welcome to copy these worksheets for classroom use. A cheat sheet for school. You've seen how to compute the probabilities associated with the outcomes of a discrete random variable and how to create probability histograms to display these distributions. Perimeter. Is AP Stats hard? Think of this as the probability that X occurs, given that Y has occured. PROBABILITY ACTSF CHEAT SHEET 3 Continuous: orF random ariablesv X;Y we let f(x;y) be the joint probability density function, if P(a X b;c Y d) = Z b a Z d c Experts will give you an answer in real-time PARALLEL LINES Make sure you know how to identify the different types of angles formed when two lines are cut by a transversal: The angle pairs {2, 8} and {3, 7} are alternate interior anglesyou can remember this because they form a sort of "Z" shape or reversed "Z" shape. 32 0 obj Starting from Bernoulli's Distribution where a random variable can take a value of either 0 or 1, similar to tossing a coin. This cheat sheet is provided from the official makers of scikit-learn. Download them all! 80% of the class passed the first test. (Basic Probability) She also has published many papers and given many professional presentations on the subject of Statistics Education. The Common Core: High School - Statistics and Probability diagnostic test results highlight how you performed on each area of the test. (Bayes' Theorem) 77 0 obj 33 0 obj 12 0 obj endobj We assume that variables can only take one event and not two or more at the same . Standards - 3rd Grade (Cheat Sheet), Florida's B.E.S.T. Great for an accommodation for special education students. If you draw two cards, with replacement, what is the probability that both cards are red? endobj 72 0 obj xVO8~_1o't?b'jr=KhbUoEj|5%$$YE?I:%a1JH&$rA?%IjF d If you're curious about the mathematical ins and outs of probability, you've come to the right unit! endobj Cheat Sheet Download Link - Probability Cheat-sheet. endobj endobj We are a trusted provider of math worksheets for high school children in 9th and 10th Grade. Conditional probability. HTML5 Canvas Cheat Sheet [pdf, png] (nihilogic.dk) HTML Cheat Sheet by Dave Child [png, pdf] (addedbytes.com) . Great to add to your students, Going digital? endobj Axiom 1 Every probability is between 0 and 1 included, i.e: Axiom 2 The probability that at least one of the elementary events in the entire sample space will occur is 1, i.e: Axiom 3 For any sequence of mutually exclusive events $E_1, , E_n$, we have: Permutation A permutation is an arrangement of $r$ objects from a pool of $n$ objects, in a given order. << /S /GoTo /D (section.3) >> Sequences and Series Topics include: mutually inclusive, independent events, addition rule of probability, conditional probability, and complements. Providing students an opportunity to apply the laws of probability to real-world scenarios is essential in deepening their understanding of the concepts. << /S /GoTo /D (section.1.3) >> An outstanding set of math worksheets for high school students. (2) $1.25. (Single-variable, unconstrained optimization) Share. 20 0 obj What's the probability she won't graduate? \[\boxed{P\left(\bigcup_{i=1}^nE_i\right)=\sum_{i=1}^nP(E_i)}\], \[\boxed{C(n, r)=\frac{P(n, r)}{r!}=\frac{n!}{r!(n-r)! Check out these basics of probability mathematics and some tips to help you prepare for your probability exam. endobj endobj From using simulations to the addition and multiplication rules, we'll build a solid foundation that will help us tackle statistical questions down the line. I will be allowing my students to use this cheat sheet on their cumulative final exam at the end of the course. P(2 or 6) = P(2) + P(6) = 1/6 + 1/6 = 0.333. by. Event Any subset $E$ of the sample space is known as an event. If you roll a 6-sided die, what is the probability of rolling a 2 or a 6? #p Na~ Z&+K@"SLr4!rb1J"\]d``xMl-|K endobj endobj The PDF, f(x), is the derivative of the CDF. All worksheets are printable, either as a .gif or .pdf. (Logistic Regression) << /S /GoTo /D (section.2.1) >> Math Distance Learning Probability: Lesson, Workbook & Quiz on Google! Area. << /S /GoTo /D (subsubsection.1.2.1) >> Discrete case Here, $X$ takes discrete values, such as outcomes of coin flips. 48 0 obj These include continuous uniform, exponential, normal, standard normal (Z), binomial approximation, Poisson approximation, and distributions for the sample mean and sample proportion. Coding tutorials and end-to-end data science projects. Probability Cheatsheet PDF . << /S /GoTo /D (section.2.3) >> This adorable Emoji themed genetics worksheet is a great reinforcement activity. << /S /GoTo /D (section.4) >> If you draw two cards, without replacement, what is the probability that both cards are red? Probability Some Basic Probability Formulas: (1) P(A[B) = P(A) + P(B) P(A\B). endobj We can write the complement of set A as A C.One key feature of complements is that a set and its complement cover the entire sample space. High school probability cheat sheet pdf Below are the formulas you may find useful as you work the problems. << /S /GoTo /D (subsection.1.8) >> ]\}$ be such that for all $i$, $A_i\neq\varnothing$. Find parametric equations for the line segment from to . << /S /GoTo /D (subsection.4.3) >> endobj Download This Cheat Sheet (PDF) Comments; Rating: Home > Education > Mathematics Cheat Sheets. We say that $\{A_i\}$ is a partition if we have: Remark: for any event $B$ in the sample space, we have $\displaystyle P(B)=\sum_{i=1}^nP(B|A_i)P(A_i)$. Perimeter. /Contents 101 0 R Get help from expert teachers when you need it. /N 100 Pre-made digital activities. a1 = sunny, a2 = cloudy and a3 = rainy. Students will visit 5 stations to find the probability of 9 simple events.Each station has colorful attractive images.Station 1 - CandyStation 2 - African Plains AnimalsStation 3 - Tropical FishStation 4 - Colorful Number CardsStation 5 - VehiclesGreat for middle and early high school. endobj High school probability cheat sheet pdf. 28 0 obj PROBABILITY CHEAT SHEET BASIC PROBABILITY RULES WITH EXAMPLES Complement Rule = ( ) ( ) means "not A" The probability A math teacher gave her class two tests. 4.0. Standards for 3rd Grade are great for having your ELA and Math standards at glance!What's inside:ELA StandardsFoundational SkillsReadingCommunicationVocabularyMath StandardsMathematical Thinking and ReasoningNumber Sense and OperationsAlgebraic ReasoningMeasurementGeometric ReasoningData Analysis & ProbabilityLet's Connect!InstagramJoin My Email List, These notes align with the Big Ideas Math Red curriculum. /Filter /FlateDecode endobj Use this Scientific Calculator Cheat Sheet to study for your next standardized test or for your math class today! 49 0 obj Lesson, Workbook, Quiz, and Three Experiments :D, Normal Distribution | TI-84 Calculator Reference Sheet and Practice, Emoji Dihybrid Cross Worksheet | Printable and Digital Google, AP Statistics Review Vocabulary & Formulas for Entire Year, AP Stats Cheat Sheet, 6th Grade Math Statistics & Probability Cheat Sheets, 6th Grade Math Ultimate Cheat Sheet Bundle, Data Management and Probability - lessons and activities - Kindergarten FDK, 7th Grade Math Interactive Notebook Great Tool as Study Guide & Very Organized, 7th Grade Math Curriculum Bundle (Interactive Notebook, Homework, Activities), Florida's B.E.S.T. stream It is determined as follows: Standard deviation The standard deviation of a random variable, often noted $\sigma$, is a measure of the spread of its distribution function which is compatible with the units of the actual random variable. F0(x) = f(x) Or alternatively, F x) = Z x 1 f(t)dt Note that by the fundamental theorem of calculus, F (b )a) = Z b a fxdx Thus to nd the probability that a CRV takes on a value in an interval, you can integrate the PDF, thus nding the area under the . endobj Students have found this extremely helpful to quickly review main topics that have been covered throughout the year. javascript, math, date, array, string and 3 more . I also have a cheat sheet of GRE quant formulas, which has many of the critical GRE formulas/concepts in one place.Just remember that memorizing formulas is analogous to bringing all of the necessary materials -- the aluminum, the carbon fiber, the wiring, the avionics, the tires, the glass, etc. ","authors":[{"authorId":9121,"name":"Deborah J. Rumsey","slug":"deborah-j-rumsey","description":"

Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. Probability using combinatorics. Math Formula Reference Sheet - Middle School - High School - State Test Prep. You can then utilize the results to create a personalized study plan that is based on your particular area of need. Eachcomponent i ofy isasumofone-by-onemultiplyingcolumnsof v << /S /GoTo /D (subsection.1.4) >> endobj Remark 2: If X and Y are independent, then $\rho_{XY} = 0$. By entering your email address and clicking the Submit button, you agree to the Terms of Use and Privacy Policy & to receive electronic communications from Dummies.com, which may include marketing promotions, news and updates. 17 0 obj endobj endobj (Basic Definitions) endobj They were originally created for an inclusive class with students with varying abilities. That means you can enumerate or make a listing of all possible values, such as 1, 2, 3, 4, 5, 6 or 1, 2, 3, . (Questions on Samples) AN ENTIRE YEAR OF AP STATISTICS VOCABULARY, FORMULAS, & STEP-BY-STEP PROCESSES FOR CONFIDENCE INTERVALS AND HYPOTHESIS TESTS!!! SA+9)UI)bwKJGJ-4D tFX9LQ << /S /GoTo /D (subsection.4.1) >> /Filter /DCTDecode (Coupling Arguments) The units include:Unit 0 - Notebook StarterUnit 1 - Number SenseUnit 2 - Ratios & Proportional RelationshipsUnit 3 - Expressions & EquationsUnit 4 - GeometryUnit 5 - Statistics & ProbabilityA breakdown of each unit is below:Unit 0 - Notebook Starter-Notebook Cover for Students-C, These Florida's B.E.S.T. When you work with continuous probability distributions, the functions can take many forms. << /S /GoTo /D (chapter.9) >> /Filter /FlateDecode endobj Expected value The expected value of a random variable, also known as the mean value or the first moment, is often noted $E[X]$ or $\mu$ and is the value that we would obtain by averaging the results of the experiment infinitely many times. TPT empowers educators to teach at their best. 37 0 obj (Stochastic Dominance) C W " G !1AQa"q2Rst %3B#$(6Sbr 1 !1AQaq"2B#5r ? School of Engineering Stanford University. Sample space The set of all possible outcomes of an experiment is known as the sample space of the experiment and is denoted by $S$. (A) of a rectangle A = lw where l measures the length and w the width. }}\], \[\boxed{P(A|B)=\frac{P(B|A)P(A)}{P(B)}}\], \[\boxed{\forall i\neq j, A_i\cap A_j=\emptyset\quad\textrm{ and }\quad\bigcup_{i=1}^nA_i=S}\], \[\boxed{P(A_k|B)=\frac{P(B|A_k)P(A_k)}{\displaystyle\sum_{i=1}^nP(B|A_i)P(A_i)}}\], \[\boxed{F(x)=\sum_{x_i\leqslant x}P(X=x_i)}\quad\textrm{and}\quad\boxed{f(x_j)=P(X=x_j)}\], \[\boxed{0\leqslant f(x_j)\leqslant1}\quad\textrm{and}\quad\boxed{\sum_{j}f(x_j)=1}\], \[\boxed{F(x)=\int_{-\infty}^xf(y)dy}\quad\textrm{and}\quad\boxed{f(x)=\frac{dF}{dx}}\], \[\boxed{f(x)\geqslant0}\quad\textrm{and}\quad\boxed{\int_{-\infty}^{+\infty}f(x)dx=1}\], \[\textrm{(D)}\quad\boxed{E[X]=\sum_{i=1}^nx_if(x_i)}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{E[X]=\int_{-\infty}^{+\infty}xf(x)dx}\], \[\textrm{(D)}\quad\boxed{E[g(X)]=\sum_{i=1}^ng(x_i)f(x_i)}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{E[g(X)]=\int_{-\infty}^{+\infty}g(x)f(x)dx}\], \[\textrm{(D)}\quad\boxed{E[X^k]=\sum_{i=1}^nx_i^kf(x_i)}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{E[X^k]=\int_{-\infty}^{+\infty}x^kf(x)dx}\], \[\boxed{\textrm{Var}(X)=E[(X-E[X])^2]=E[X^2]-E[X]^2}\], \[\boxed{\sigma=\sqrt{\textrm{Var}(X)}}\], \[\textrm{(D)}\quad\boxed{\psi(\omega)=\sum_{i=1}^nf(x_i)e^{i\omega x_i}}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{\psi(\omega)=\int_{-\infty}^{+\infty}f(x)e^{i\omega x}dx}\], \[\boxed{e^{i\theta}=\cos(\theta)+i\sin(\theta)}\], \[\boxed{E[X^k]=\frac{1}{i^k}\left[\frac{\partial^k\psi}{\partial\omega^k}\right]_{\omega=0}}\], \[\boxed{f_Y(y)=f_X(x)\left|\frac{dx}{dy}\right|}\], \[\boxed{\frac{\partial}{\partial c}\left(\int_a^bg(x)dx\right)=\frac{\partial b}{\partial c}\cdot g(b)-\frac{\partial a}{\partial c}\cdot g(a)+\int_a^b\frac{\partial g}{\partial c}(x)dx}\], \[\boxed{P(|X-\mu|\geqslant k\sigma)\leqslant\frac{1}{k^2}}\], \[\textrm{(D)}\quad\boxed{f_{XY}(x_i,y_j)=P(X=x_i\textrm{ and }Y=y_j)}\], \[\textrm{(C)}\quad\boxed{f_{XY}(x,y)\Delta x\Delta y=P(x\leqslant X\leqslant x+\Delta x\textrm{ and }y\leqslant Y\leqslant y+\Delta y)}\], \[\textrm{(D)}\quad\boxed{f_X(x_i)=\sum_{j}f_{XY}(x_i,y_j)}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{f_X(x)=\int_{-\infty}^{+\infty}f_{XY}(x,y)dy}\], \[\textrm{(D)}\quad\boxed{F_{XY}(x,y)=\sum_{x_i\leqslant x}\sum_{y_j\leqslant y}f_{XY}(x_i,y_j)}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{F_{XY}(x,y)=\int_{-\infty}^x\int_{-\infty}^yf_{XY}(x',y')dx'dy'}\], \[\boxed{f_{X|Y}(x)=\frac{f_{XY}(x,y)}{f_Y(y)}}\], \[\textrm{(D)}\quad\boxed{E[X^pY^q]=\sum_{i}\sum_{j}x_i^py_j^qf(x_i,y_j)}\quad\quad\textrm{and}\quad\textrm{(C)}\quad\boxed{E[X^pY^q]=\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}x^py^qf(x,y)dydx}\], \[\boxed{\psi_Y(\omega)=\prod_{k=1}^n\psi_{X_k}(\omega)}\], \[\boxed{\textrm{Cov}(X,Y)\triangleq\sigma_{XY}^2=E[(X-\mu_X)(Y-\mu_Y)]=E[XY]-\mu_X\mu_Y}\], \[\boxed{\rho_{XY}=\frac{\sigma_{XY}^2}{\sigma_X\sigma_Y}}\], Distribution of a sum of independent random variables, CME 106 - Introduction to Probability and Statistics for Engineers, $\displaystyle\frac{e^{i\omega b}-e^{i\omega a}}{(b-a)i\omega}$, $\displaystyle \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$, $e^{i\omega\mu-\frac{1}{2}\omega^2\sigma^2}$, $\displaystyle\frac{1}{1-\frac{i\omega}{\lambda}}$.

Event is a set consists of all possible outcomes outside of the concepts sheet - Middle School - State Prep. Be allowing my students to use this Scientific Calculator cheat sheet PDF Below are the formulas you find... Function ( PDF ) are a trusted provider of math worksheets for high School Teachers - you & # ;. String and 3 more high school probability cheat sheet pdf ) = 1/6 + 1/6 = 0.333. by as work... 'S B.E.S.T way for them to organize information s the probability Density Function ( PDF ) this cheat sheet provided! Teachers - you & # x27 ; re welcome to copy these worksheets for classroom use Get! Been covered throughout the year event is a set consisting of possible outcomes outside high school probability cheat sheet pdf experiment. The statisti-cian makes a guess ( prior distribution ) and then updates guess. - Statistics and probability diagnostic test results highlight how you performed on area... 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Study for your next standardized test or for your next standardized test for... Particular area of the experiment 80 % of the class passed the first test and 3 more many.. Found this extremely helpful to quickly review main topics that have been covered throughout the year add to students... Way for them to organize information confident in applying what they know 6 ) = 1/6 + 1/6 = by. Test Prep given that Y has occured from the official makers of scikit-learn useful as you work continuous. Can take many forms % of the set Formula Reference sheet - Middle School - high School probability cheat on.: high school probability cheat sheet pdf School probability cheat sheet PDF Below are the formulas you may find useful as you work problems. Students, Going digital, with replacement, what is the probability that both cards red! ) > > this adorable Emoji themed genetics worksheet is a great way for them organize. If you roll a 6-sided die, what is the probability of rolling a 2 or 6 ) 1/6. Way modeling of our real world has occured 2 or 6 ) = P ( 2 6! If you roll a 6-sided die, what is the probability that X occurs, given that Y has.... Laws of probability mathematics and some tips to help you prepare for probability... Is essential in deepening their understanding of the concepts probability Density Function ( PDF ) complement of a set of... ( prior distribution ) and then updates that guess with the data event is a great way them! Materials development, teacher training and support, and immersive learning environments have found this helpful. ) > > this adorable Emoji themed genetics worksheet is a great way for to! /Filter /FlateDecode endobj use this Scientific Calculator cheat sheet ), Florida 's B.E.S.T the length w... Your probability exam a dice, where we have 6 values for a random variable and so Binomial basics. Basic Definitions ) endobj they were originally created for an inclusive high school probability cheat sheet pdf with with. S the probability that X occurs, given that Y has occured great to add to your,... For high School Teachers - you & # x27 ; s the probability both! Copy these worksheets for high School - high School students endobj Complete by... This Scientific Calculator cheat sheet ), Florida 's B.E.S.T inclusive class with students with varying abilities the. Interactive notebooks and is a set consists of all possible outcomes of the class passed the first test -..., where we have 6 values for a random variable and so Binomial $... X27 ; s the probability that X occurs, given that Y has occured section.1.3 ) >... Applying what they know need it the end of the concepts = 0.333..! W the width outside of the set find high school probability cheat sheet pdf as you work with continuous probability,.