Our recent determination of a Salpeter slope for the IMF in the field of 30Doradus (Selman and Melnick 2005) appears to be in conflict with simpleprobabilistic counting arguments advanced in the past to support observationalclaims of a steeper IMF in the LMC field. In this paper we re-examine thesearguments and show by explicit construction that, contrary to these claims, thefield IMF is expected to be exactly the same as the stellar IMF of the clustersout of which the field was presumably formed. We show that the current data onthe mass distribution of clusters themselves is in excellent agreement with ourmodel, and is consistent with a single spectrum {\it by number of stars} of thetype $n^\beta$ with beta between -1.8 and -2.2 down to the smallest clusterswithout any preferred mass scale for cluster formation. We also use the randomsampling model to estimate the statistics of the maximal mass star in clusters,and confirm the discrepancy with observations found by Weidner and Kroupa(2006). We argue that rather than signaling the violation of the randomsampling model these observations reflect the gravitationally unstable natureof systems with one very large mass star. We stress the importance of therandom sampling model as a \emph{null hypothesis} whose violation would signalthe presence of interesting physics.
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机译：我们最近确定的30Doradus领域的IMF的Salpeter斜率（Selman和Melnick 2005）似乎与过去提出的支持LMC领域中更陡峭的IMF的简单概率计数论证相冲突。在本文中，我们重新检查了这些论点，并通过明确的构造表明，与这些主张相反，该场IMF预期与推测形成该场的星团的恒星IMF完全相同。我们显示，关于星团本身质量分布的当前数据与我们的模型非常吻合，并且与类型为$ n ^ \ beta $且β在-1.8和-2.2之间的单个光谱{\ it by star number}一致。下降到最小的团簇，而没有任何优选的团簇形成质量尺度。我们还使用随机抽样模型来估计星团中最大质量恒星的统计数据，并根据Weidner和Kroupa（2006）的观察结果来确认差异。我们认为，这些观察结果反映了具有一个非常大质量恒星的系统的重力不稳定特性，而不是暗示违反了随机采样模型。我们强调随机抽样模型作为\ emph {null hypothesis}的重要性，违反该规则将表明存在有趣的物理现象。
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