rand function

Non-central Chi square distribution

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This post contains interactive python code which you can execute in the browser itself. 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 … Read more

Chi square distribution – demystified

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A random variable is always associated with a probability distribution. When the random variable undergoes mathematical transformation the underlying probability distribution no longer remains the same. Consider a random variable $latex Z$ whose probability distribution function (PDF) is a standard normal distribution ($latex \mu=0$ and $latex \sigma^2=1$). Now, if the random variable is squared (a … Read more

Uniform random variable

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Uniform random variables are used to model scenarios where the expected outcomes are equi-probable. For example, in a communication system design, the set of all possible source symbols are considered equally probable and therefore modeled as a uniform random variable. The uniform distribution is the underlying distribution for an uniform random variable. A continuous uniform … Read more