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Compute the probability distribution, expectation, and variance of the following random variable: - Multipliying the result...

Compute the probability distribution, expectation, and variance of the following random variable:

- Multipliying the result of rolling two dice.

Solutions

Expert Solution

below is the probability distribution of rolling two dice:

x P(x)
1    1/36
2    1/18
3    1/18
4    1/12
5    1/18
6    1/9
8    1/18
9    1/36
10    1/18
12    1/9
15    1/18
16    1/36
18    1/18
20    1/18
24    1/18
25    1/36
30    1/18
36    1/36
x f(x) xP(x) x2P(x)
1    1/36 0.028 0.028
2    1/18 0.111 0.222
3    1/18 0.167 0.500
4    1/12 0.333 1.333
5    1/18 0.278 1.389
6    1/9 0.667 4.000
8    1/18 0.444 3.556
9    1/36 0.250 2.250
10    1/18 0.556 5.556
12    1/9 1.333 16.000
15    1/18 0.833 12.500
16    1/36 0.444 7.111
18    1/18 1.000 18.000
20    1/18 1.111 22.222
24    1/18 1.333 32.000
25    1/36 0.694 17.361
30    1/18 1.667 50.000
36    1/36 1.000 36.000
total 12.250 230.028
E(x) =μ= ΣxP(x) = 12.2500
E(x2) = Σx2P(x) = 230.0278
Var(x)=σ2 = E(x2)-(E(x))2= 79.9653

from abvoe expectation =12.25

Variance =79.9653

milcah answered 1 month ago
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