= Solution
Writing $Y_i$ for `team1_goal` and $x_i$ for `team1_xg`, the first hypothesis concerns only the <expected value>:
$$
H_1:\quad \mathbb E(Y_i\mid x_i)=x_i
\quad\text{for every }i.
$$
The second specifies the entire conditional <probability distribution>:
$$
H_2:\quad Y_i\mid x_i\sim\operatorname{Pois}(x_i)
\quad\text{for every }i,
$$
with independence between matches as assumed in the question. The <Poisson limit theorem>, often called the law of small numbers in this setting, suggests a <Poisson distribution> when a goal count is the sum of many approximately independent rare scoring opportunities.
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