Statistics

Normal Distribution – Numerical Problems with Solutions

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Normal Distribution – Numerical Problems with Solutions Author: Bindeshwar Singh Kushwaha Platform: PostNetwork Academy 1. Definition of Normal Distribution A continuous random variable $X$ follows a Normal Distribution with mean $\mu$ and variance $\sigma^2$ if its probability density function (PDF) is: $$ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{ -\frac{(x – \mu)^2}{2\sigma^2} }, \quad -\infty < x […]

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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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Naive Bayes Classification Algorithm for Weather Dataset

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Naive Bayes Classification Algorithm for Weather Dataset Author: Bindeshwar Singh Kushwaha | PostNetwork Academy Introduction to Naive Bayes Classifier Naive Bayes is a probabilistic classification algorithm. It is based on Bayes’ Theorem and the naive independence assumption. Suppose we have a feature vector \(\mathbf{X} = (x_1, x_2, …, x_n)\) and a class \(y\). Bayes Theorem:

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Poisson Distribution Numerical Examples

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📘 Poisson Distribution Numerical Examples Author: Bindeshwar Singh Kushwaha Institution: PostNetwork Academy Example 1: Truck Arrivals The number of heavy trucks arriving at a railway station follows a Poisson distribution with an average of 2 arrivals per hour. Find: (a) Probability that no truck arrives (b) Probability that at least two trucks arrive Let \(

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Binomial Distribution Mean and Variance Related Problems| Data Sc. and A.I. Lect. Series

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Binomial Distribution: Mean and Variance Problem 1: Mean = 3, Variance = 4? Given: Is it possible a binomial distribution has a mean of 3 and a variance of 4? Solution: Mean: \( \mu = np \) Variance: \( \sigma^2 = npq \), where \( q = 1 – p \) Given: \( np =

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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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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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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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