Cheatsheet - Summary Discrete Mathematics I stream Counting mainly encompasses fundamental counting rule, the permutation rule, and the combination rule. 592 \renewcommand{\iff}{\leftrightarrow} Assume that s is not 0. 1.1 Additive and Multiplicative Principles 1.2 Binomial Coefficients 1.3 Combinations and Permutations 1.4 Combinatorial Proofs 1.5 Stars and Bars 1.6 Advanced Counting Using PIE Set DifferenceDifference between sets is denoted by A B, is the set containing elements of set A but not in B. i.e all elements of A except the element of B.ComplementThe complement of a set A, denoted by , is the set of all the elements except A. Complement of the set A is U A. GroupA non-empty set G, (G, *) is called a group if it follows the following axiom: |A| = m and |B| = n, then1. &@(BR-c)#b~9md@;iR2N {\TTX|'Wv{KdB?Hs}n^wVWZND+->TLqzZt,[kS3#P:OJ6NzW"OR]a'Q~%>6 in the word 'READER'. cheat sheet From a night class at Fordham University, NYC, Fall, 2008. WebThe ultimate cheat sheet - the shortest possible document which basically covers all of maths from say algebra to whatever comes after calculus. Hence, the total number of permutation is $6 \times 6 = 36$. It is determined as follows: Characteristic function A characteristic function $\psi(\omega)$ is derived from a probability density function $f(x)$ and is defined as: Euler's formula For $\theta \in \mathbb{R}$, the Euler formula is the name given to the identity: Revisiting the $k^{th}$ moment The $k^{th}$ moment can also be computed with the characteristic function as follows: Transformation of random variables Let the variables $X$ and $Y$ be linked by some function. Cartesian ProductsLet A and B be two sets. Learn more. /N 100 Prove that if xy is irrational, then y is irrational. Graphs 82 7.2. Discrete Mathematics Cheat Sheet - DocDroid Course Hero is not sponsored or endorsed by any college or university. WebThe Discrete Math Cheat Sheet was released by Dois on Cheatography. For solving these problems, mathematical theory of counting are used. Here's how they described it: Equations commonly used in Discrete Math. We have: Covariance We define the covariance of two random variables $X$ and $Y$, that we note $\sigma_{XY}^2$ or more commonly $\textrm{Cov}(X,Y)$, as follows: Correlation By noting $\sigma_X, \sigma_Y$ the standard deviations of $X$ and $Y$, we define the correlation between the random variables $X$ and $Y$, noted $\rho_{XY}$, as follows: Remark 1: we note that for any random variables $X, Y$, we have $\rho_{XY}\in[-1,1]$. stream (c) Express P(k + 1). Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. discrete math counting cheat sheet.pdf - | Course Hero Discrete Math 1: Set Theory. Cheat Sheet | by Alex Roan - Medium WebCheat Sheet of Mathemtical Notation and Terminology Logic and Sets Notation Terminology Explanation and Examples a:=b dened by The objectaon the side of the colon is dened byb. Hence, a+c b+d(modm)andac bd(modm). That is, an event is a set consisting of possible outcomes of the experiment. Discrete Mathematics Problem 2 In how many ways can the letters of the word 'READER' be arranged? ~C'ZOdA3,3FHaD%B,e@,*/x}9Scv\`{]SL*|)B(u9V|My\4 Xm$qg3~Fq&M?D'Clk +&$.U;n8FHCfQd!gzMv94NU'M`cU6{@zxG,,?F,}I+52XbQN0.''f>:Vn(g."]^{\p5,`"zI%nO. 5 0 obj Binomial Coecients 75 5.5. /Parent 22 0 R /CreationDate (D:20151115165753Z) For $k, \sigma>0$, we have the following inequality: Discrete distributions Here are the main discrete distributions to have in mind: Continuous distributions Here are the main continuous distributions to have in mind: Joint probability density function The joint probability density function of two random variables $X$ and $Y$, that we note $f_{XY}$, is defined as follows: Marginal density We define the marginal density for the variable $X$ as follows: Cumulative distribution We define cumulative distrubution $F_{XY}$ as follows: Conditional density The conditional density of $X$ with respect to $Y$, often noted $f_{X|Y}$, is defined as follows: Independence Two random variables $X$ and $Y$ are said to be independent if we have: Moments of joint distributions We define the moments of joint distributions of random variables $X$ and $Y$ as follows: Distribution of a sum of independent random variables Let $Y=X_1++X_n$ with $X_1, , X_n$ independent. Discrete Math 1: Set Theory Cheat Sheet Photo by Gabby K from Pexels (not actually discrete math) 1. /Contents 25 0 R <> \[\boxed{P\left(\bigcup_{i=1}^nE_i\right)=\sum_{i=1}^nP(E_i)}\], \[\boxed{C(n, r)=\frac{P(n, r)}{r!}=\frac{n!}{r!(n-r)! In this case it is written with just the | symbol. $A \cap B = \emptyset$), then mathematically $|A \cup B| = |A| + |B|$, The Rule of Product If a sequence of tasks $T_1, T_2, \dots, T_m$ can be done in $w_1, w_2, \dots w_m$ ways respectively and every task arrives after the occurrence of the previous task, then there are $w_1 \times w_2 \times \dots \times w_m$ ways to perform the tasks. Types of propositions based on Truth values1.Tautology A proposition which is always true, is called a tautology.2.Contradiction A proposition which is always false, is called a contradiction.3.Contingency A proposition that is neither a tautology nor a contradiction is called a contingency. /ImageMask true From a set S ={x, y, z} by taking two at a time, all permutations are , We have to form a permutation of three digit numbers from a set of numbers $S = \lbrace 1, 2, 3 \rbrace$.
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