Aggregate data frame by date and apply different functions to corresponding columns?

I have the following data frame "DF" which is part of a much larger one:

             X1  X2            X3 X4 X5
4468 2010-03-24   3  1.000000e+00  1  2
7662 2010-03-24   9  3.000000e+00  2  1
1272 2010-03-25   8  2.000000e+00  1  1
1273 2010-03-26   9  0.000000e+00  1  1
1274 2010-03-27   8  0.000000e+00  1  1
4469 2010-03-28   4  0.000000e+00  1  2
7663 2010-03-28   4  3.000000e+00  3  1
8734 2010-03-28   7  4.000000e+00  2  3
1275 2010-03-29   8  0.000000e+00  1  1

As you can see the first column contains a date. What I want to do is as follows: I want to transform this dataframe to a new one "DF2" where there is only 1 row per date with corresponding column values:

X2, the average 
X3, the sum
X4, the maximum

of all previous values per date. X5 is not relevant and can be removed. This would be the result:

             X1  X2            X3 X4
7662 2010-03-24   6  4.000000e+00  2  
1272 2010-03-25   8  2.000000e+00  1  
1273 2010-03-26   9  0.000000e+00  1  
1274 2010-03-27   8  0.000000e+00  1  
8734 2010-03-28   5  7.000000e+00  3  
1275 2010-03-29   8  0.000000e+00  1  

Does anyone know how to accomplish this? Help would be much appreciated!