Question

In: Statistics and Probability

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.

Solutions

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

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