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Variance and Covariance
Variance Variance means spread of a distribution Let X be a random variable with mean μ. The variance of X
Expectation
The expected value, or mean, or first moment, of X is defined to beassuming that the sum (or integral) is
Transformation of Random Variables
Suppose X is a random variable with PDF fX and CDF FX. Let Y = r(X) be a function of
Independent Random Variables and Conditional Distribution
Independent Random Variables Two random variables are X and Y are independent if, for every A and B,P(X ∈ A,
Bivariate and Marginal Distribution
Joint Mass Function Remember the probability mass function definition. That is the study of one random variable. Given two discrete
Continuous Random Variables
Uniform Probability Distribution X has Uniform(a, b) distribution, written X~Uniform(a, b), ifwhere a < b. The distribution function is The
Discrete Random Variables
In this section, we are going to cover some important Discrete Random Variables. Note that we will be writing X
Introduction to Random Variables
Random Variable A random variable is a mappingX : Ω→Rthat assigns a real number X(ω) to each outcome ω Getting
Bayes’ Theorem
A partition of Ω is a sequence of disjoint sets A1, A2, … such that The Law of Total Probability
Introduction to Probability – 2
Uniform Probability distribution If Ω is finite and each outcome is equally likely then, where |A| denotes the number of elements in
Introduction to Probability
Probability quantifies uncertainty. It is a measure of “how likely” an “event” can occur. Probability is measured on a scale