Use the original df1 indexes to create the series:
df1['e'] = pd.Series(np.random.randn(sLength), index=df1.index)
Edit 2015
Some reported getting the SettingWithCopyWarning with this code.
However, the code still runs perfectly with the current pandas version 0.16.1.
>>> sLength = len(df1['a'])
>>> df1
a b c d
6 -0.269221 -0.026476 0.997517 1.294385
8 0.917438 0.847941 0.034235 -0.448948
>>> df1['e'] = pd.Series(np.random.randn(sLength), index=df1.index)
>>> df1
a b c d e
6 -0.269221 -0.026476 0.997517 1.294385 1.757167
8 0.917438 0.847941 0.034235 -0.448948 2.228131
>>> p.version.short_version
'0.16.1'
The SettingWithCopyWarning aims to inform of a possibly invalid assignment on a copy of the Dataframe. It doesn't necessarily say you did it wrong (it can trigger false positives) but from 0.13.0 it let you know there are more adequate methods for the same purpose. Then, if you get the warning, just follow its advise: Try using .loc[row_index,col_indexer] = value instead
>>> df1.loc[:,'f'] = pd.Series(np.random.randn(sLength), index=df1.index)
>>> df1
a b c d e f
6 -0.269221 -0.026476 0.997517 1.294385 1.757167 -0.050927
8 0.917438 0.847941 0.034235 -0.448948 2.228131 0.006109
>>>