Stats doubt - finding expectation

[Homer Simpson]

In a random throw of n die, obtain the expectation of: (a) the sum of points on them (b) the product of points of them. How to do this??

[Akshay Jain]

The no. Of elements in the sample space is 6^n
consider this ques when n=2
the expectd sum is 7 which is equal to the average of highest sum + the lowest sum
and if u notice that the prob distribution od this is symmetrical about mean sum

if n=3 then also apply same logic....expected sum= 10.5

so the requared expectation is  (n+6*n)/2=7n/2

[Amit Goyal]

Let X(i) be the random variable that takes the value equal to the number that appears on the ith dice. We are interested in finding
E(X(1)  + X(2) + X(3) + .... + X(n))
= E(X(1)) + E(X(2)) + .... + E(X(n))  
= 7/2 + 7/2 + ... + 7/2
= (7n)/2

Since X(1), X(2), ... , X(n) are independent,
E(X(1)X(2)...X(n)) = E(X(1))E(X(2))...E(X(n)) = (7/2)^n

[Homer Simpson]

thank you! i got it now :)