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i.e. Tossing a fair coin

$p_H =$ probability of heads $= 0.5$

$L(p_H | HH) = P(X = HH | p_H) $

$= 0.25$

Okay, right-hand of equation I understand,

$P(X = HH | p_H) = 0.25 =$ probability of "$X = HH$" given $p_H$

but what does the value resulting from the left side mean if it's not probability.

$L(p_H | HH) = 0.25 =$ Likelihood of $p_H$ given we observed $HH$ is $0.25$ ??

What does that even mean? Certainly it's not the same as $P(p_H | HH)$

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    $\begingroup$ stats.stackexchange.com/questions/2641/… $\endgroup$ – David Jan 15 at 18:21
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    $\begingroup$ weird that didn't show up when i was typing the question $\endgroup$ – NoName Jan 15 at 18:27
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    $\begingroup$ Agreed: it looks like the pop-up search is pretty bad. $\endgroup$ – whuber Jan 15 at 18:46