Probability and Statistics

Normal Distribution – Numerical Problems with Solutions

Artificial Intelligence, Machine Learning, Probability and Statistics /

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

Artificial Intelligence, Machine Learning, Machine Learning, Mathematics, Probability and Statistics, Research and Development, Statistics /

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

Probability and Statistics, Statistics /

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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Geometric Distribution Made Simple | Stepwise Approach #176 Data Sc. and A.I. Lect. Series

Algebra, Artificial Intelligence, Machine Learning, Probability and Statistics /

  Geometric Distribution Made Simple | Stepwise Approach Bindeshwar Singh Kushwaha PostNetwork Academy  Geometric Distribution Let a sequence of Bernoulli trials be performed, each with constant probability \(p\) of success and \(q = 1 – p\) of failure. Trials are independent, and we continue performing them until the first success occurs. Let \(X\) be the

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Hypergeometric Distribution A Distribution of Dependent Events #175 Data Sc. and A.I. Lect. Series

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    Hypergeometric Distribution : A Distribution of Dependent Events By Bindeshwar Singh Kushwaha PostNetwork Academy Introduction In the previous sections, we studied distributions such as the binomial distribution. The binomial distribution assumes that each trial is independent and the probability of success remains constant. However, in many real-life problems, selections are made without replacement.

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Learn about the Discrete Uniform Distribution in probability and statistics with detailed explanations, examples, formulas, and visualizations. Understand its mean, variance, and applications such as die rolls and expected frequency calculations. Presented by Bindeshwar Singh Kushwaha, PostNetwork Academy.

Discrete Uniform Distribution in Statistics

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Discrete Uniform Distribution By: Bindeshwar Singh Kushwaha PostNetwork Academy Discrete Uniform Distribution A random variable \( X \) is said to have a discrete uniform distribution if it takes integer values from \( a \) to \( b \) with equal probability. The number of possible values is \[ n = b – a +

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Fitting of Poisson Distribution

Fitting of Poisson Distribution

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Fitting of Poisson Distribution Bindeshwar Singh Kushwaha — PostNetwork Academy Introduction Master the technique of fitting the Poisson distribution to real-world frequency data. This tutorial shows a step-by-step method to calculate theoretical frequencies for observed datasets. Key Concepts & Techniques Introduction to Fitting: Fit a theoretical Poisson distribution to experimental data to derive expected frequencies.

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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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Poisson Distribution | Data Sc. and A.I. Lect. Series

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📘 Understand Poisson Distribution 📌 Introduction In binomial distributions, events’ occurrences and non-occurrences are equally important. However, in real-life situations: Events do not occur as outcomes of fixed number of trials. Events occur randomly over time. Interest lies only in the number of occurrences. Examples: Number of printing mistakes per page in a book. Number

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

Artificial Intelligence, Machine Learning, Probability and Statistics /

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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