Notation for likelihood function In Wikipedia there is a chart of

the likelihood function $p^2_H$ for the probability of a coin landing
heads-up (without prior knowledge of the coin's fairness) given that
we have observed HH

Why is this function denoted as $p^2_H$ ? 
i.e why little p and why raised to the power of 2?

 A: Quoting the entire Wikipedia section:

Consider a simple statistical model of a coin flip: a single parameter $ p_\text{H}$ that expresses the "fairness" of the coin. The parameter is the probability that a coin lands heads up ("H") when tossed. ${\displaystyle p_{\text{H}}}$ can take on any value within the range $0.0$ to $1.0$. For a perfectly fair coin, $p_\text{H} = 0.5$.
Imagine flipping a fair coin twice, and observing the following data: two heads in two tosses ("HH"). Assuming that each successive coin flip is i.i.d., then the probability of observing HH is
$$
    {\displaystyle P({\text{HH}}\mid p_{\text{H}}=0.5)=0.5^{2}=0.25.}
$$
Hence, given the observed data HH, the likelihood that the model parameter $p_\text{H}$ equals 0.5 is 0.25. Mathematically, this is written as
$${\displaystyle {\mathcal {L}}(p_{\text{H}}=0.5\mid {\text{HH}})=0.25.}
$$
This is not the same as saying that the probability that $p_\text{H} = 0.5$, given the observation HH, is $0.25$. (For that, we could apply Bayes' theorem, which implies that the posterior probability is proportional to the likelihood times the prior probability.)
Suppose that the coin is not a fair coin, but instead it has ${\displaystyle p_{\text{H}}=0.3}$. Then the probability of getting two heads is
$$
{\displaystyle P({\text{HH}}\mid p_{\text{H}}=0.3)=0.3^{2}=0.09.}
$$
Hence
$${\displaystyle {\mathcal {L}}(p_{\text{H}}=0.3\mid {\text{HH}})=0.09.}$$
More generally, for each value of $p_\text{H}$, we can calculate the corresponding likelihood. The result of such calculations is displayed in Figure 1.

It thus makes quite clearly the point that the likelihood is the probability of observing two heads up in a row, i.e., the square of the probability ${\displaystyle p_{\text{H}}}$ that a coin lands heads up, i.e., ${\displaystyle p_{\text{H}}^2}$. The example is intended as an illustration of the likelihood function
\begin{align*}
{\mathcal {L}}\,:\, [0,1]&\longmapsto \mathbb R\\
p_H&\longmapsto {\displaystyle {\mathcal {L}}(p_{\text{H}})}=p_{\text{H}}^2
\end{align*}
and of the fact that this function is not a probability density in the parameter $p_{\text{H}}$. (Or a cumulative distribution function.) But it is the probability of the event "HH" occurring, seen as a function of $p_{\text{H}}$.
One interesting feature of the example is that the likelihood function is not explicitly connected with the outcome of a random variable $X$ or a random sample $X_1,\ldots,X_n$ but directly with the coin flipping experiment. For instance, if the outcome of the experiment was "HT", heads up followed by tails up, the likelihood function associated with this event would be
\begin{align*}
{\mathcal {L}}\,:\, [0,1]&\longmapsto \mathbb R\\
p_{\text{H}}&\longmapsto {\displaystyle {\mathcal {L}}(p_{\text{H}})}=p_{\text{H}}(1-p_{\text{H}})
\end{align*}
(which no longer looks like a cdf!)
while the likelihood function associated with the realisation of the (deduced) random variable counting the number of heads out of two tosses, $X=1$, would be
\begin{align*}
{\mathcal {L}}\,:\, [0,1]&\longmapsto \mathbb R\\
p_{\text{H}}&\longmapsto {\displaystyle {\mathcal {L}}(p_{\text{H}})}=2 p_{\text{H}}(1-p_{\text{H}})
\end{align*}
