linear algebra - Should the formula for the inverse of a 2x2 matrix be obvious?

pr.likelihood – Intuition behind the noncentral chi sq. as Poisson mixing Answer

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pr.likelihood – Intuition behind the noncentral chi sq. as Poisson mixing

It is understood (cf. Wikipedia, Noncentral_chi_distribution) that the non-central chi-square distribution with ok levels of liberty is a Poisson weighted blend of central chi-squared distributions).

There are many proofs however all are principally the identical (behold identical ref part “Derivation of the pdf” for a sketch and right here libre stats for a freely accessible full proof).

I’m searching for the instinct behind this outcome, that’s, a route to construe and elucidate it. Otherwise such the outcome appears kindly of accident. Any thought ?

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G.

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