2. Correct. The answer is false
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
F(x)=
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.