Take 3 dice and throw these dice 30 times. Let X be the sum of the...

Take 3 dice and throw these dice 30 times. Let X be the sum of the number of dots on upper faces of the dice.

Obtain probability distribution of X. Also find mean and variance.

Expert Solution

X	fav cases	p(x)	X.p(x)	X^2.P(x)
3	1	0.00463	0.00463	0.00463
4	3	0.013889	0.041667	0.125
5	6	0.027778	0.166667	1
6	10	0.046296	0.462963	4.62963
7	15	0.069444	1.041667	15.625
8	21	0.097222	2.041667	42.875
9	25	0.115741	2.893519	72.33796
10	27	0.125	3.375	91.125
11	27	0.125	3.375	91.125
12	25	0.115741	2.893519	72.33796
13	21	0.097222	2.041667	42.875
14	15	0.069444	1.041667	15.625
15	10	0.046296	0.462963	4.62963
16	6	0.027778	0.166667	1
17	3	0.013889	0.041667	0.125
18	1	0.00463	0.00463	0.00463
	216	1	20.05556	455.4444

There is one possible way three dice can total 3
3 ways for 4
6 for 5
10 for 6
15 for 7
21 for 8
25 for 9
27 for 10
27 for 11
25 for 12
21 for 13
15 for 14
10 for 15
6 for 16
3 for 17
1 for 18

orchestra answered 2 years ago

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