Question

A fair die is rolled twice. What is the conditional expectation of the sum of the two
outcomes given the first roll shows a 1?

Answer 1

What is the expectation of the result of one single die?

Answer 2

Balenator i would say the answer is 11/36

Answer 3

E(X+Y | X=1) = E(1+Y) = 1 + E(Y)

So what is E(Y) ?

Answer 4

would e(y) be 1/6?

Answer 5

I got 3.5 for E(x+Y), so i would i just do 3.5/E(X=1)?

Answer 6

if the first die shows 1
then the sum of the two dice will be
2,3,4,5,6,7
all equally likely
and the expected value is the average of those numbers

Answer 7

yes
so the expected value would be 3.5

Answer 8

I get 27/6 = 9/2 = 4.5

Answer 9

oh sorry i forgot to add 1 to all the them

Answer 10

1/6(1+1)+1/6(1+2)....+1/6(1+6)

Answer 11

would i just divide that by 1/6 since E(x=1) equals 1/6?

Answer 12

you do (just as you wrote)
1/6(1+1)+1/6(1+2)....+1/6(1+6)

which is the same as doing (2+3+4+5+6+7)/6
we use 1/6 because each sum is equally likely

the E(x=1) = 1/6 does not matter, because we are told:
given that the first roll is 1
(it does not matter if it's unlikely or it happens all the time... once it happens, we now concentrate on what to expect for the sum of the two dice)

Answer 13

in class we were taught to divide by the given probability, which in this case is (X=1)/ so it would just be 4.5?

Answer 14

yes, the answer is 4.5

Answer 15

the conditional expectation of the sum of two dice when the first die shows 1 is given, is 4.5

Answer 16

okay thanks