Question 1058040
{{{N=3*5*2=30}}}
30 possible solutions in the sample space.
Assume that 1 is the correct answer for each question, all other numbers are incorrect answers.
1,1,1
1,1,2
1,2,1
1,2,2
1,3,1
1,3,2
1,4,1
1,4,2
1,5,1
1,5,2
2,1,1
2,1,2
2,2,1
2,2,2
2,3,1
2,3,2
2,4,1
2,4,2
2,5,1
2,5,2
3,1,1
3,1,2
3,2,1
3,2,2
3,3,1
3,3,2
3,4,1
3,4,2
3,5,1
3,5,2
So then looking at the distribution of correct answers,
3,1
2,7
1,14
0,8
c) {{{E(X)=3*(1/30)+2*(7/30)+1*(14/30)+0*(8/30)=31/30}}}
{{{E(X^2)=9*(1/30)+4*(7/30)+1*(14/30)+0*(8/30)=51/30=17/10}}}
{{{V(X)=E(X^2)-(E(X))^2=17/10-(31/30)^2=1530/900-961/900=569/900}}}
d) What are you looking for here?