Frequency of letters change by the length of the texts? In terms of the frequency of letters, how is it possible to have different frequent letters when the length of the text I'm analyzing is shorter? 

At the moment, I'm comparing the frequencies of a long text and a subtext from that text. To my surprise, the most frequent letters changed. In the long one it was the letter e followed by the letter t, however in the small text it was t followed by e. Also, when I checked the frequency of different types of texts (e.g news articles), the frequency of letters also changed as well as the most frequent one.

The bottom line is, how can that be possible? It makes no sense to me.
Letter frequency checks how often a letter appears in your text.  Depending on your text, the frequency of letters will change.  If your text is short and has the name "Alex" in it a lot, it will make the frequency of the letter X much higher than average.  Generally when discussing the expected letter frequency, people refer to the average letter frequency that appears in the english language (http://en.wikipedia.org/wiki/Letter_frequency).  Though for specific texts the fequency might not be close to the average, and with shorter texts the frequency might be dramatically different, overall the frequency of a long passage should be close to the average.