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role playing games like dungeons & dragons use many different types of dice. suppose that a...

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role playing games like dungeons & dragons use manydifferent types of dice. suppose that a SIX sided die has facesmarked 1,2,3,4,5,6. The intelligence of a character is determinedby rolling this die twice and adding 1 to the sum of the spots. Thefaces are equally likely and the two rolls are independent. what isthe average (mean) intelligence for such characters?

how spread out are their intelligence , as measured by thestandard deviation of the distribution?(round your answer to fourdecimal places)

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3.8 Ratings (452 Votes)

here let X is sum of two scores ;

below is probability distribution of X:

x f(x) xP(x) x2P(x)
2.0000    1/36 0.056 0.111
3.0000    1/18 0.167 0.500
4.0000    1/12 0.333 1.333
5.0000    1/9 0.556 2.778
6.0000    5/36 0.833 5.000
7.0000    1/6 1.167 8.167
8.0000    5/36 1.111 8.889
9.0000    1/9 1.000 9.000
10.0000    1/12 0.833 8.333
11.0000    1/18 0.611 6.722
12.0000    1/36 0.333 4.000
total 7.000 54.833
E(x) =μ= ΣxP(x) = 7.0000
E(x2) = Σx2P(x) = 54.8333
Var(x)=σ2 = E(x2)-(E(x))2= 5.8333
std deviation=         σ= √σ2 = 2.4152

as intelligence score :Y =X+1

hence therefore mean of Y =E(X+1)=E(X)+1 =7+1 =8

and std deviation =SD(X+1)=SD(X)=2.4152
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