## Normal (Gaussian) Distribution: Everything you need to know

Normal or Gaussian distribution is one of the most widely used distribution functions in statistics. This post covers all the

Continue ReadingNormal or Gaussian distribution is one of the most widely used distribution functions in statistics. This post covers all the

Continue ReadingThe Weak Law of Large Numbers (WLLN) If X1, X2, . . . , Xn are IID, then This theorem

Continue ReadingPointwise or sure convergence A sequence of random variables {Xn}n∈N is said to converge point-wise or surely to X if Xn(ω) → X(ω), ∀

Continue ReadingMarkov’s Inequalities Let X be a non-negative random variable and suppose that E(X) exists. For any t > 0, Chebyshev’s

Continue ReadingVariance Variance means spread of a distribution Let X be a random variable with mean μ. The variance of X

Continue ReadingThe expected value, or mean, or first moment, of X is defined to beassuming that the sum (or integral) is

Continue ReadingSuppose X is a random variable with PDF fX and CDF FX. Let Y = r(X) be a function of

Continue ReadingLet X = (X1, . . . , Xn) where X1, . . . , Xn are random variables. We

Continue ReadingIndependent Random Variables Two random variables are X and Y are independent if, for every A and B,P(X ∈ A,

Continue ReadingJoint Mass Function Remember the probability mass function definition. That is the study of one random variable. Given two discrete

Continue ReadingUniform Probability Distribution X has Uniform(a, b) distribution, written X~Uniform(a, b), ifwhere a < b. The distribution function is The

Continue ReadingIn this section, we are going to cover some important Discrete Random Variables. Note that we will be writing X

Continue ReadingRandom Variable A random variable is a mappingX : Ω→Rthat assigns a real number X(ω) to each outcome ω Getting

Continue ReadingPartition A partition of Ω is a sequence of disjoint sets A1, A2, … such that The Law of Total

Continue ReadingUniform Probability distribution If Ω is finite and each outcome is equally likely then, where |A| denotes the number of elements in

Continue ReadingProbability quantifies uncertainty. It is a measure of “how likely” an “event” can occur. Probability is measured on a scale

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