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  "body": "\n## Summary\n\nThe noncentral chi-squared distribution is the distribution of a sum of squares of independent normal variables with unit variance and arbitrary means.\nIt has two parameters: the number $k$ of terms and the noncentrality $\\lambda$, the sum of the squared means.\nFor $\\lambda = 0$ it is the ordinary chi-squared distribution.\nIt describes the distribution of chi-squared test statistics under alternatives, so it is used to compute the power of these tests.\n\n## Explanations\n\n### L1 human\n\nThrow a dart at a target in $k$ dimensions, with independent normal errors in each direction, but aim at a point at distance $\\sqrt{\\lambda}$ from the centre.\nThe squared distance of the dart from the centre has the noncentral chi-squared distribution.\nWhen the aim is at the centre, this is the usual chi-squared distribution.\nFor example, if $X$ is normal with mean $2$ and variance $1$, then $X^2$ is noncentral chi-squared with $k = 1$ and $\\lambda = 4$, and its mean is $1 + 4 = 5$.\n",
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