16 questions linked to/from sum of noncentral Chi-square random variables
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### Is there a PDF for a generalized non-central chi-squared distribution [duplicate]

Is there a PDF for a distribution defined as a sum of squares of random variables pulled from a family of normal distributions with different standard deviation? Is there a way of analytically ...
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### non-central Chi-square distribution [duplicate]

If $X \sim \mathcal{N}(\mu,\sigma^2)$ where $\mu > 0$ and $\sigma > 2$, how do I find the PDF of $X^2$, and will it correspond to non-central Chi-square distribution?
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### What is the distribution of $(X−Y)^2+(Z−Y)^2$, where $X$,$Y$ and $Z$ are independent normal distributions with their own means and variance? [duplicate]

I came up with a question: What is the distribution of $(X−Y)^2+(Z−Y)^2$, where $X$,$Y$ and $Z$ are independent normal distributions with their own means and variance? The common part is $Y$ in both ...
1 vote
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### Density Function of $T = (\bar{x})^2$ where $\bar{x}$ $\sim$ $N(\mu, 1/n)$ [duplicate]

Suppose we have $\bar{x}$ $\sim$ $N(\mu, 1/n)$, its pdf then is $f(\bar{x}) = \sqrt{\frac{n}{2\pi}}e^{-n(\bar{x}-\mu)^2/2}$ Let $T = (\bar{x})^2$, we want to calculate its pdf. My first thought is: ...
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### Distribution of the square of a non-standard normal random variable

What is the distribution of the square of a non-standard normal random variable (i.e., the mean is not equal to 0 and the variance is not equal to 1)?
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### What is the distribution of the sum of squared chi-square random variables?

What would be the distribution of the following equation: $$y = a^2 + 2ad + d^2$$ where $a$ and $d$ are independent non-central chi-square random variables with $2 \textbf{M}$ degrees of freedom. ...
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