2. Incorrect. The answer is false, not true


The distribution function is defined as follows: F(x)=P(X≤x)=Su≤xf(u). Then, from results of problem 1, we find that:


0, -∞<x<2

1/36, 2≤x<3

3/36, 3≤x<4

6/36, 4≤x<5


35/36, 11≤x<12

1, 12≤x<∞.


The density and distribution function of X are shown below:


Remember that X is a discrete random variable, so the lines which join the dots of both graphs are not part of the functions.