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    $\begingroup$ It's because you're not using Mathjax to construct it, which you really should do for all your math related stuff. $\endgroup$
    – jbowman
    Commented May 20 at 21:08
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    $\begingroup$ I cannot figure out what your table means: it doesn't appear to specify any kind of distribution. Could you explain? $\endgroup$
    – whuber ♦
    Commented May 20 at 21:31
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    $\begingroup$ Could you please explain what your table showing a "map of samples to statistic" means? Because a statistic is, by definition, a numerical function of the sample and no such function is in evidence (what are the "$t_i$"?), it takes considerable guessing to read this post. You could further clarify it by using $\TeX$ markup to render the mathematical symbols as intended. $\endgroup$
    – whuber ♦
    Commented Jun 6 at 11:23
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    $\begingroup$ @whuber I use this definition of sufficient statistic as given in Casella: A statistic $T(X)$ is a sufficient statistic for $\theta$ if the conditional distribution of the sample $X$ given the value of $T(X)$ does not depend on $θ$. ie $P(X=x|T(X)=T(x);\theta=\theta_1)=P(X=x|T(X)=T(x);\theta=\theta_2)$ . But we can see in my example that $P(X=x1|T(X)=t1;\theta=\theta1)=0.1/(0.1+0.2) = 1/3$ , which is not equal to $P(X=x1|T(X)=t1;\theta=\theta2)=0.2/(0.2+0.2)=1/2$ $\endgroup$
    – Shreyans
    Commented Jun 26 at 22:13
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    $\begingroup$ @Shreyans, it seems to me that you are right and wikipedia is wrong. I really don't understand their discussion of priors in the earlier paragraph, which is out-of-scope. The characterization they give for sufficiency seems to instead match identifiability? But I wonder if part of the issue here is that they have butchered the truth. I vaguely recall there being a relationship between sufficiency, completeness and some mapping being injective / surjective. Isn't that in the Casella book? I'll try to recall all I've forgotten on this topic. Maybe we should rewrite the page when we are done here $\endgroup$
    – Guillaume Dehaene
    Commented Jun 27 at 9:27