# Questions tagged [chi-squared]

Use this tag for questions about (1) distributions of a sum of squares of independent standard normal random variables or (2) statistical hypothesis tests with such a sampling distribution if the null hypothesis is true.

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### reading my p-value from chi-square vs my polt data

I'm a bit confused with the result I get and wonder if someone can put light into my understanding. consider the following table (neighborhood vs education level): ...
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### Multivariate Generalized Chi-square distribution

A generalized chi-squared distributed random variable $\xi$ can be expressed as $$\xi=q(x)=x'Q_2x+q_1'x+q_0,$$ where $x\sim\mathcal{N}\left(\mu, \Sigma\right)$, $Q_2$ is a matrix, $q_1$ is a vector ...
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### Logarithm of normal distribution is constant plus Chi squared?

I'm reading Bayesian data analysis. On page 85 it is stated that "In the d dimensional normal distribution, the logarithm of the density function is a constant plus a $χ^2_d$ distribution divided ...
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### Distribution of normalised chi-square distribution

I'm doing a data analysis where the data is right-skewed, similar to a $\chi^2$-distribution. The data is then normalised to their z-scores. $z = \frac{X-\mu}{\sigma}$ I want to do an outlier analysis ...
1 vote
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### Expectation of logarithm function with chi-square distributed variables

How to calculate $\mathbb{E}\left[\log\left(1+x\right)\right]$ where $x$ denotes a central chi-square distributed variable? The lower bound and upper bound of this expectation are also of my concern.
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### Finding P($X^2$<1) , after verifying that $X^2$ is distributed $\chi^2_1$
The Problem Suppose $X$ and $Y$ are independent n(0,1) random variables. Find $P(X^2 < 1)$, after verifying that $X^2$ is distributed $\chi^2_1$. My Work I understand that I need to find the ...
### Why is the chi-square distribution skewed to the right and why does it only range from $0$ to $\infty$?
My book says that the chi-squared distribution is continuous, skewed to the right, and ranges from $0$ to $\infty$ with no explanation what-so-ever. It just gives me a table to tell me how to find \$P(\...