Question

In: Advanced Math

Determine the entropy of the random variable which counts the sum of three dice.

Determine the entropy of the random variable which counts the sum of
three dice.

Expert Solution

Sum of three die has possibilities 3,4,5..18

The entropy is therefore given below:

X	p(X)	-XP(X)
3	0.00463	7.003361
4	0.013889	7.42933
5	0.027778	7.781513
6	0.046296	8.006723
7	0.069444	8.108537
8	0.097222	8.097876
9	0.115741	8.428624
10	0.125	9.0309
11	0.125	9.93399
12	0.115741	11.23816
13	0.097222	13.15905
14	0.069444	16.21707
15	0.046296	20.01681
16	0.027778	24.90084
17	0.013889	31.57465
18	0.00463	42.02017

Sum of the values is (sum of third column) is given below:

is the required entropy of the random variable

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Colby Messinger answered 3 years ago

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