Probability

Formulas are organized based on their importance in the CAT exam.
1 Covariance with a Constant
2 MGF of a Linear Transformation
3 Covariance of a Sum
4 Independent Events
5 Fourth Central Moment
6 Simple Event
7 Likelihood
8 Conditional Expectation
9 MSE Bias-Variance Decomposition
10 Symmetry of Independence
11 Second Central Moment
12 Covariance Bound
13 CDF for a Continuous Variable
14 Addition rule for three events
15 Complementary probability
16 Bayes Factor
17 Odds Form of Bayes' Theorem
18 Zero Covariance
19 Correlation Range
20 Correlation Coefficient
21 Variance of Sample Mean
22 Independent events (two events)
23 Conditional Independence
24 Independence Implies Zero Covariance
25 Indicator Random Variable
26 Random Variable
27 Weak Law of Large Numbers
28 Continuous Random Variable
29 Variance of an Indicator
30 Poisson Process Stationary Increments
31 Normal PDF
32 Poisson PMF
33 Conditional Complement
34 Permutation Formula
35 Variance of Independent Indicators
36 Variance and standard deviation
37 Expectation of an Indicator
38 Probability Density Function
39 Binomial PMF
40 PMF Non-Negativity
41 Binomial Variance
42 De Morgan's Second Law
43 Binomial Standard Deviation
44 Binomial Probability of No Success
45 Bernoulli Mean
46 PDF Non-Negativity
47 Binomial Mean
48 Classical probability definition
49 Binomial Probability of At Least One Success
50 Joint PMF
51 Addition rule for two events
52 Discrete Random Variable
53 Probability of a Complement of an Intersection
54 Expectation of a Function
55 Hypergeometric Distribution
56 Conditional Definition of Independence
57 Standard Normal Distribution
58 Marginal PDF
59 Central Moment
60 Bernoulli Random Variable
61 PMF Normalization
62 Binomial Probability of All Successes
63 Continuity Correction
64 Binomial Coefficient Recurrence
65 Beta-Gamma Relationship
66 Markov's Inequality
67 Variance Decomposition
68 Hypergeometric Variance
69 Normal Distribution
70 Joint Distribution
71 Conditional Covariance
72 Chebyshev's Inequality
73 Binomial Standardization
74 Bias of an Estimator
75 Conditional probability
76 Probability Mass Function
77 Probability of at least one event
78 Binomial distribution
79 Cumulative Distribution Function
80 Linearity of Expectation
81 Variance of Poisson Process Count
82 Sample Standard Deviation
83 Independence of Complements
84 Variance of Independent Variables
85 MGF of a Constant
86 Poisson Additivity
87 Standardization of a Normal Variable
88 Marginalization
89 Strong Law of Large Numbers
90 Variance of a Sum of Indicators
91 Coefficient of Variation
92 Variance of a Constant
93 Memoryless Property
94 Union with Complement
95 Quantile Function
96 Intersection with Complement
97 Continuous Joint Expectation
98 Expectation of a Discrete Random Variable
99 Negative Binomial Random Variable
100 Expectation of discrete random variable
101 Joint PDF
102 Law of Total Covariance
103 One-Sided Chebyshev Inequality
104 Poisson Approximation to Binomial
105 Poisson Variance
106 Normal Variance
107 Joint CDF
108 First Raw Moment
109 Jensen's Inequality
110 Poisson Process Independent Increments
111 Posterior Probability
112 Covariance of Linear Transformations
113 Sum of Indicators
114 MGF and Moments
115 Pairwise Independence
116 Covariance
117 CDF Limits
118 Geometric Variance
119 Compound Event
120 Complement Probability Rule
121 Cauchy-Schwarz Inequality
122 Discrete random variable distribution
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