Probability Archives - GaussianWaves https://www.gaussianwaves.com/category/probability/ Signal Processing for Communication Systems Thu, 06 Jul 2023 11:30:58 +0000 en-US hourly 1 https://wordpress.org/?v=6.4.4 https://i0.wp.com/www.gaussianwaves.com/gaussianwaves/wp-content/uploads/2016/02/cropped-gaussianwaves_logo_120_120.png?fit=32%2C32&ssl=1 Probability Archives - GaussianWaves https://www.gaussianwaves.com/category/probability/ 32 32 163393712 Bayes’ theorem https://www.gaussianwaves.com/2021/04/bayes-theorem/ https://www.gaussianwaves.com/2021/04/bayes-theorem/#comments Sat, 17 Apr 2021 13:48:29 +0000 https://www.gaussianwaves.com/?p=29510 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

The post Bayes’ theorem appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2021/04/bayes-theorem/feed/ 3 29510 Hidden Markov Models (HMM) – Simplified !!! https://www.gaussianwaves.com/2020/03/hidden-markov-models-hmm-simplified/ https://www.gaussianwaves.com/2020/03/hidden-markov-models-hmm-simplified/#comments Tue, 17 Mar 2020 05:08:35 +0000 https://www.gaussianwaves.com/?p=22270 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

The post Hidden Markov Models (HMM) – Simplified !!! appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2020/03/hidden-markov-models-hmm-simplified/feed/ 3 22270 Markov Chains – Simplified !! https://www.gaussianwaves.com/2020/03/markov-chains-simplified/ https://www.gaussianwaves.com/2020/03/markov-chains-simplified/#respond Fri, 06 Mar 2020 07:11:37 +0000 https://www.gaussianwaves.com/?p=22215 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 Assume that we want to model the ... Read more

The post Markov Chains – Simplified !! appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2020/03/markov-chains-simplified/feed/ 0 22215 Exponential random variable – simulation & application https://www.gaussianwaves.com/2019/07/exponential-random-variable/ https://www.gaussianwaves.com/2019/07/exponential-random-variable/#respond Fri, 26 Jul 2019 05:51:23 +0000 https://www.gaussianwaves.com/?p=20310 Introduction An exponential random variable (RV) is a continuous random variable that has applications in modeling a Poisson process. Poisson processes find extensive applications in tele-traffic modeling and queuing theory. They are used to model random points in time or space, such as the times when call requests arriving at an exchange, the times when ... Read more

The post Exponential random variable – simulation & application appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2019/07/exponential-random-variable/feed/ 0 20310 Binomial random variable using Matlab https://www.gaussianwaves.com/2019/07/binomial-random-variable/ https://www.gaussianwaves.com/2019/07/binomial-random-variable/#respond Thu, 25 Jul 2019 06:57:14 +0000 https://www.gaussianwaves.com/?p=20290 Binomial random variable, a discrete random variable, models the number of successes in mutually independent Bernoulli trials, each with success probability . The term Bernoulli trial implies that each trial is a random experiment with exactly two possible outcomes: success and failure. It can be used to model the total number of bit errors in ... Read more

The post Binomial random variable using Matlab appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2019/07/binomial-random-variable/feed/ 0 20290 Bernoulli random variable https://www.gaussianwaves.com/2019/07/bernoulli-random-variable/ https://www.gaussianwaves.com/2019/07/bernoulli-random-variable/#respond Tue, 23 Jul 2019 05:40:32 +0000 https://www.gaussianwaves.com/?p=20285 Bernoulli random variable is a discrete random variable with two outcomes – success and failure, with probabilities p and (1-p). It is a good model for binary data generators and also for modeling bit error patterns in the received binary data when a communication channel introduces random errors. To generate a Bernoulli random variable X, ... Read more

The post Bernoulli random variable appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2019/07/bernoulli-random-variable/feed/ 0 20285 Plot histogram and estimated PDF in Matlab https://www.gaussianwaves.com/2016/10/how-to-use-histogram-function-in-matlab-to-plot-the-estimated-pdf-curve/ https://www.gaussianwaves.com/2016/10/how-to-use-histogram-function-in-matlab-to-plot-the-estimated-pdf-curve/#respond Thu, 06 Oct 2016 07:40:37 +0000 http://www.gaussianwaves.com/?p=12831 Key focus: With examples, let’s estimate and plot the probability density function of a random variable using Matlab histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability density function ... Read more

The post Plot histogram and estimated PDF in Matlab appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2016/10/how-to-use-histogram-function-in-matlab-to-plot-the-estimated-pdf-curve/feed/ 0 12831 White Noise : Simulation and Analysis using Matlab https://www.gaussianwaves.com/2013/11/simulation-and-analysis-of-white-noise-in-matlab/ https://www.gaussianwaves.com/2013/11/simulation-and-analysis-of-white-noise-in-matlab/#comments Fri, 29 Nov 2013 08:09:46 +0000 http://www.gaussianwaves.com/?p=4254 Definition A random process (or signal for your visualization) with a constant power spectral density (PSD) function is a white noise process. Power Spectral Density Power Spectral Density function (PSD) shows how much power is contained in each of the spectral component. For example, for a sine wave of fixed frequency, the PSD plot will ... Read more

The post White Noise : Simulation and Analysis using Matlab appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2013/11/simulation-and-analysis-of-white-noise-in-matlab/feed/ 33 4254 Introduction to concepts in probability https://www.gaussianwaves.com/2013/10/introduction-to-concepts-in-probability/ https://www.gaussianwaves.com/2013/10/introduction-to-concepts-in-probability/#respond Wed, 09 Oct 2013 09:02:43 +0000 http://www.gaussianwaves.com/?p=3697 What is Probability? Probability is a branch of mathematics that deals with uncertainty. The term “probability” is used to quantify the degree of belief or confidence that something is true (or false). It gives us the likelihood of occurrence of a given event. It is expressed as a number that could take any value in ... Read more

The post Introduction to concepts in probability appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2013/10/introduction-to-concepts-in-probability/feed/ 0 3697 Non-central Chi square distribution https://www.gaussianwaves.com/2012/09/non-central-chi-squared-distribution/ https://www.gaussianwaves.com/2012/09/non-central-chi-squared-distribution/#respond Mon, 24 Sep 2012 09:17:50 +0000 http://www.gaussianwaves.com/?p=2299 If squares of k independent standard normal random variables are added, it gives rise to central Chi-squared distribution with ‘k’ degrees of freedom. Instead, if squares of k independent normal random variables with non-zero means are added, it gives rise to non-central Chi-squared distribution. Non-central Chi-square distribution is related to Ricean distribution, whereas the central ... Read more

The post Non-central Chi square distribution appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/09/non-central-chi-squared-distribution/feed/ 0 2299