You\'re playing Dungeons and Dragons, an old-school pen-and-paper role playing g

Question

You're playing Dungeons and Dragons, an old-school pen-and-paper role playing game. The game uses an 8-sided die, with the numbers 1-8 on each face. The probability of rolling each number is 1/8 11. Let Y equal the sum of the values from two independent rolls, then E[Y] is a. 3.5 b. 4.5 c. 7.0 d. 7.5 e. 9.0 12. What is the variance of one throw of the die? a. 4.75 b. 5.25 c. 5.60 d. 5.85 e. 6.10 13. Suppose the result of #12 was some number we'll call K. Then, what is the variance of Y, as defined in #11? b. 2K c. 3K d. 4K e. 5K

Explanation / Answer

11) as expected value of one dice E(X)=(1+2+3+4+5+6+7+8)/8=4.5

hence sum of values =4.5+4.5=9

option E

12)

E(X2)=(12+22+32+42+52+62+72+82)/8=25.5

hence Variance(X)=E(X2)-(E(X))2 =5.25

option b

13)

option b

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