# Math Help - 10 Sided Die

1. ## 10 Sided Die

Say we have a ten sided die.

Teacher wants us to find the prob mass function. Thats easy... f(u)=1/10 for 1,2,3,4,5,6,7,8,9,10.

We know E(U) is the mean = 5.5

How do we figure out something like...

E(2U-7)

or

E(U^2 +4)

2. Originally Posted by DINOCALC09
Say we have a ten sided die.

Teacher wants us to find the prob mass function. Thats easy... f(u)=1/10 for 1,2,3,4,5,6,7,8,9,10.

We know E(U) is the mean = 5.5

How do we figure out something like...

E(2U-7)

or

E(U^2 +4)
E(aX + b) = a E(X) + b.

E(U^2 + 4) = E(U^2) + 4. To get E(U^2) you first need to construct the pmf of U^2 from the pmf of U.

3. Are the answers 4.0 and 42.5 respectively?

4. Originally Posted by DINOCALC09
Are the answers 4.0 and 42.5 respectively?
I don't do arithmetic. If you post working that clearly shows where these answers have come from, someone will tell you if the working is OK (and, one would assume, if the working is OK then the answers will be OK).

5. we know E(U) = 5.5

So E(2U-7) = 2E(U)-7 = 2*5.5-7 = 4

Then E(U^2 + 4) = E(U^2)+4 = [(n+1)(2n+1)]/6 + 4 = 38.5 + 4 = 42.5

THANKS

6. Originally Posted by DINOCALC09
we know E(U) = 5.5

So E(2U-7) = 2E(U)-7 = 2*5.5-7 = 4

Then E(U^2 + 4) = E(U^2)+4 = [(n+1)(2n+1)]/6 + 4 = 38.5 + 4 = 42.5 Mr F says: This line does not (for me at least) satisfy my request "... post working that clearly shows where these answers have come from". I doubt your instructor would be too happy with it either.

THANKS
..

7. formula in the book after manipulating the variance forumula.

[1^2 + 2^2 + ... + n^2]/n

[n(n+1)(2n+1)]/6n

[(n+1)(2n+1)]/6

(n^2 -1)/12

10 sides of a die, hence n = 10

8. Originally Posted by DINOCALC09
formula in the book after manipulating the variance forumula.

[1^2 + 2^2 + ... + n^2]/n

[n(n+1)(2n+1)]/6n

[(n+1)(2n+1)]/6

(n^2 -1)/12 Mr F says: I have no idea where this line has come from.
10 sides of a die, hence n = 10