Probability

Formulas are organized based on their importance in the CAT exam.
1 Union with Complement
2 Covariance with a Constant
3 Simple Event
4 MGF of a Linear Transformation
5 MSE Bias-Variance Decomposition
6 Independent Events
7 Symmetry of Independence
8 Odds Form of Bayes' Theorem
9 Covariance of a Sum
10 Conditional Expectation
11 CDF for a Continuous Variable
12 Bayes Factor
13 Second Central Moment
14 Likelihood
15 Fourth Central Moment
16 Zero Covariance
17 Covariance
18 Covariance Bound
19 Correlation Coefficient
20 Complementary probability
21 Addition rule for three events
22 Correlation Range
23 Independent events (two events)
24 Variance of Sample Mean
25 Conditional Independence
26 Independence Implies Zero Covariance
27 Weak Law of Large Numbers
28 Indicator Random Variable
29 Random Variable
30 Continuous Random Variable
31 Variance of an Indicator
32 Normal PDF
33 Conditional Complement
34 Poisson PMF
35 Poisson Process Stationary Increments
36 Permutation Formula
37 Variance of Independent Indicators
38 Expectation of an Indicator
39 Variance and standard deviation
40 Probability Density Function
41 Binomial PMF
42 Binomial Variance
43 De Morgan's Second Law
44 Binomial Standard Deviation
45 PMF Non-Negativity
46 Bernoulli Mean
47 Binomial Probability of No Success
48 PDF Non-Negativity
49 Binomial Mean
50 Classical probability definition
51 Binomial Probability of At Least One Success
52 Joint PMF
53 Discrete Random Variable
54 Probability of a Complement of an Intersection
55 Expectation of a Function
56 Hypergeometric Distribution
57 Conditional Definition of Independence
58 Standard Normal Distribution
59 Marginal PDF
60 Central Moment
61 Bernoulli Random Variable
62 Addition rule for two events
63 Binomial Coefficient Recurrence
64 Beta-Gamma Relationship
65 Markov's Inequality
66 Variance Decomposition
67 Hypergeometric Variance
68 Normal Distribution
69 Chebyshev's Inequality
70 PMF Normalization
71 Conditional probability
72 Probability of at least one event
73 Binomial distribution
74 Cumulative Distribution Function
75 Conditional Covariance
76 Binomial Standardization
77 Bias of an Estimator
78 Joint Distribution
79 Binomial Probability of All Successes
80 Probability Mass Function
81 Independence of Complements
82 Variance of a Constant
83 Linearity of Expectation
84 Variance of Independent Variables
85 Sample Standard Deviation
86 Variance of Poisson Process Count
87 MGF of a Constant
88 Poisson Additivity
89 Coefficient of Variation
90 Variance of a Sum of Indicators
91 Strong Law of Large Numbers
92 Standardization of a Normal Variable
93 Marginalization
94 Memoryless Property
95 Intersection with Complement
96 Continuous Joint Expectation
97 Expectation of a Discrete Random Variable
98 Negative Binomial Random Variable
99 Expectation of discrete random variable
100 Poisson Approximation to Binomial
101 One-Sided Chebyshev Inequality
102 Joint PDF
103 Poisson Variance
104 Normal Variance
105 Joint CDF
106 Poisson Process Independent Increments
107 First Raw Moment
108 Jensen's Inequality
109 Posterior Probability
110 Covariance of Linear Transformations
111 Pairwise Independence
112 MGF and Moments
113 Continuity Correction
114 Law of Total Covariance
115 CDF Limits
116 Geometric Variance
117 Compound Event
118 Quantile Function
119 Sum of Indicators
120 Cauchy-Schwarz Inequality
121 Discrete random variable distribution
122 Complement Probability Rule
123 Probability of At Least One Event
124 Median of a Distribution
125 Probability Range
126 Joint Probability of Independent Events
127 Expected Number of Successes
128 Inclusion-Exclusion for Three Events
129 CDF Monotonicity
130 Impossible Event
131 Probability of the Sample Space
132 Prior Probability
133 PDF Normalization
134 Bayes' Theorem
135 CDF for a Discrete Variable
136 Addition Axiom
137 Random Experiment
138 CDF Range
139 Geometric Mean
140 Complement of an Event
141 Probability of an Event
142 Bernoulli PMF
143 Probability Generating Function
144 Sample Space
145 Mutually Exclusive Events
146 Discrete Uniform Mean
147 Gamma Mean
148 Inclusion-Exclusion for Two Events
149 Addition Rule for Two Events
150 Gamma Variance
151 Normal Symmetry
152 Negative Binomial Variance
153 Geometric Random Variable
154 Law of Total Expectation
155 PGF and Factorial Moments
156 Complement Method
157 De Morgan's First Law
158 Negative Binomial Mean
159 Continuous Uniform Variance
160 Conditional PDF
161 Exponential Survival Function
162 Multiplication Rule
163 Hypergeometric Mean
164 Exponential Variance
165 Exponential Memoryless Property
166 Sum of Expectations
167 Certain Event
168 Counting Rule for Ordered Outcomes
169 Expectation of a Continuous Random Variable
170 Variance
171 Covariance Symmetry
172 Standard Deviation
173 Mean Squared Error
174 Characteristic Function
175 CLT Approximation for a Sum
176 Probability of a Complement of a Union
177 Beta Distribution
178 Law of Total Variance
179 Characteristic Function of a Sum
180 Exponential Mean
181 Conditional Variance
182 Continuous Uniform Distribution
183 Birthday-Type Probability
184 Variance Shortcut Formula
185 Independence Versus Uncorrelatedness
186 Expected Value of a Binomial Coefficient
187 Multiplication rule for n independent events
188 Beta Function
189 Probability from a PDF
190 Outcome
191 Total Number of Subsets
192 Central Limit Theorem
193 Binomial Coefficient Symmetry
194 Probability of Difference of Events
195 Gamma Function for Integers
196 Discrete Total Expectation
197 Negative Binomial PMF
198 Hypergeometric PMF
199 Poisson Random Variable
200 Binomial-Poisson Approximation
201 Expected Value of a Constant
202 Probability of the Empty Set
203 Multiplication rule for two events
204 Continuous Function Expectation
205 Total probability theorem
206 Bayes' theorem
207 Continuous Total Expectation
208 Conditional Union Rule
209 Variance of a Sum
210 Poisson Mean
211 Normal Approximation to Binomial
212 Geometric PMF
213 Beta Variance
214 Alternative Multiplication Rule
215 Variance of a Linear Transformation
216 General Inclusion-Exclusion
217 Continuous Uniform Mean
218 Gamma Function
219 Conditional Expectation for Continuous Variables
220 PGF and Mean
221 CLT Approximation for Sample Mean
222 Probability Model
223 Probability from a PMF
224 Kurtosis
225 r-th Raw Moment
226 Event
227 Third Central Moment
228 Conditional Expectation for Discrete Variables
229 Discrete Uniform Distribution
230 Normal Distribution Interval Probability
231 MGF of a Sum of Independent Variables
232 Sample Mean
233 Addition Rule for Mutually Exclusive Events
234 Bernoulli Variance
235 Conditional PMF
236 Skewness
237 Expected Sample Mean
238 Expected Poisson Process Count
239 Marginal PMF
240 Poisson Standard Deviation
241 Discrete Uniform Variance
242 Excess Kurtosis
243 Unbiased Estimator
244 Conditional Probability
245 Mutual Independence
246 Partition of Sample Space
247 Bayes' Theorem with a Partition
248 Probability at a Single Point
249 Joint Expectation
250 Moment Generating Function
251 Exponential Distribution
252 Interval Probability Using CDF
253 Normal Mean
254 Binomial Random Variable
255 Gamma Distribution
256 Independence of Random Variables
257 Exponential CDF
258 Standard Error of the Mean
259 Beta Mean
260 Combination Formula
261 Covariance Shortcut Formula
262 Sample Variance
263 Exponential-Poisson Connection
264 Poisson Process Count Distribution
265 Law of Total Probability