Probability

Implementing Markov Chain in Python

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Keywords: Markov Chain, Python, probability, data analysis, data science Markov Chain Markov chain is a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. This article is about implementing Markov chain in Python Markov chain is described in one of the earlier posts. For better understanding … Read more

Bayes’ theorem

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Key focus: Bayes’ theorem is a method for revising the prior probability for specific event, taking into account the evidence available about the event. Introduction In statistics, the process of drawing conclusions from data subject to random variations – is called “statistical inference”. Usually, in any random experiment, the observations are recorded and conclusions have … Read more

Hidden Markov Models (HMM) – Simplified !!!

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Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t observe them directly. These hidden events need to be inferred. For example, given a sentence in a natural language we only observe the … Read more

Markov Chains – Simplified !!

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Key focus: Markov chains are a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. ● Time-series data like speech, stock price movements.● Words in a sentence.● Base pairs on the rung of a DNA ladder. States and transitions: markov chains Assume that we want to … Read more

Histogram to PDF in Matlab — normalize bins and overlay the theoretical curve

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Turn a Matlab histogram into an estimated PDF: normalize by sample count and bin width, then overlay normpdf / theoretical densities for Gaussian, Rayleigh, and exponential checks.

Derive BPSK BER – optimum receiver in AWGN channel

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BPSK Lab path:Derive BER (theory) → AWGN noise model → BER simulation (Python & Matlab)Tools: BER vs Eb/N0 calculator · Shannon capacity Key focus: Derive BPSK BER (bit error rate) for optimum receiver in AWGN channel. Explained intuitively step by step. BPSK modulation is the simplest of all the M-PSK techniques. An insight into the … Read more