1a. .976
1b. .188
1c. .212
1d. .8197

2a. {0,1,2,3,4,5}
2b. P(N=k) = (6-k)/21
2c. 1/4

3a. .45
3b. 3/5
3c. 5/36

4a. .878
4b. F(x) = 0 if x < 0
           .1 if x=0
           1-.9e^(-2x) if x > 0
4c. .45

5a. E(Y)=22.5  and V(Y)=3.75
5b. .8664
 
6a. c=1/2
6b. P(X-2Y<1) = int_0^(1/3) int_(-x)^x (1/2)e^(-x) dy dx
                + int_(1/3)^(infinity) int_((x-1)/2)^x (1/2)e^(-x) dy dx
6c f_Y(y) = (1/2) e^(-y) if y > 0
            (1/2) e^(y) if y<0
6d. P(X-2Y > 1 | Y=1) = P(X>3 | Y=1) = e^(-2) 

7a. E(N) = 1
7b. V(N) = 1