Statistics

Normal Distribution A Detailed Step-by-Step Explanation

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Normal Distribution A Detailed Step-by-Step Explanation By Bindeshwar Singh Kushwaha PostNetwork Academy Introduction: Random Variables A random variable (r.v.) is a function that assigns a numerical value to each outcome of a random experiment. There are two main types of random variables: Discrete Random Variable: Takes countable values (e.g., number of heads in 3 coin […]

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Negative Binomial Distribution | Simple Explanation #177 Data Sc. and A.I. Lect. Series

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Negative Binomial Distribution A Detailed Step-by-Step Explanation By Bindeshwar Singh Kushwaha PostNetwork Academy Introduction: Relation with Geometric Distribution The negative binomial distribution is a generalization of the geometric distribution. It describes the number of failures before the \( r^{th} \) success in a sequence of Bernoulli trials. When \( r = 1 \), it reduces

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Text Classification with Bag of Words and Naive Bayes

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Text Classification with Bag of Words and Naive Bayes Author: Bindeshwar Singh Kushwaha | PostNetwork Academy Understanding Text with Machine Learning Processing and understanding text allows extraction of meaningful information from raw data. Text data can be structured into features that machine learning algorithms can analyze. Machine learning approaches include supervised, unsupervised, and deep learning

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Fitting Binomial Distribution | Data Science and A.I. Lecture Series

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Fitting Binomial Distribution Introduction Fitting a binomial distribution involves comparing observed frequencies with expected frequencies derived from the binomial probability formula. The recurrence relation simplifies the process of finding probabilities. This technique is useful for testing if a dataset follows a binomial distribution. Binomial Probability Function The binomial probability function is: $$p(x) = {n \choose

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Moment Generating Function of Binomial Distribution

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Moment Generating Function of Binomial Distribution Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Definition of Moment Generating Function The moment generating function (m.g.f.) of a random variable \( X \) is defined as: \[ M_X(t) = E(e^{tX}) \] For a continuous random variable: \[ M_X(t) = \int_{-\infty}^{\infty} e^{tx} f(x) \, dx \] For a discrete

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Moments of Binomial Distribution Video I Data Science and A.I. Lect. Series

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  Moments of Binomial Distribution By Bindeshwar Singh Kushwaha — PostNetwork Academy Moment Definition Let \( X \sim B(n, p) \) be a binomial random variable. The \( r^\text{th} \) raw moment about origin: \( \mu_r’ = \mathbb{E}(X^r) = \sum_{x=0}^{n} x^r \cdot \mathbb{P}(X = x) \) First-order moment (mean): \( \mu_1′ = \mathbb{E}(X) \) Binomial

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Binomial Distribution Data Science and A.I. Lecture Series

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  Binomial Distribution Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha | PostNetwork Academy Binomial Probability Function The binomial probability function is given by: \[ P(X = k) = \binom{n}{k} p^k (1 – p)^{n – k} \] where: \( n \) = total number of trials \( k \) = number of successes

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Bernoulli Distribution in Probability and Statistics

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Bernoulli Distribution Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha | PostNetwork Academy Introduction to Bernoulli Distribution A Bernoulli trial is an experiment with only two possible outcomes: Success (1) and Failure (0). If p is the probability of success, then q = 1 – p is the probability of failure. A random

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Addition, Multiplication Theorem of Expectation and Covariance

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Addition, Multiplication Theorem of Expectation and Covariance Data Science and A.I. Lecture Series By Bindeshwar Singh Kushwaha PostNetwork Academy Outline Introduction Addition Theorem of Expectation Proof of Addition Theorem Multiplication Theorem of Expectation Proof of Multiplication Theorem Covariance Introduction Expectation (or expected value) is a fundamental concept in probability and statistics. It provides a measure

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