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Following is the probability distribution for age of a student at a certain public high school.
X
13
14
15
16
17
18
P(x) 0.09 0.22 0.24 0.28 0.15 0.02

(a) Find the variance of the ages. Round the answer to at least four decimal places.
The variance of the ages is

Following is the probability distribution for age of a student at a certain public high school X 13 14 15 16 17 18 Px 009 022 024 028 015 002 a Find the varianc class=

Respuesta :

Considering the given discrete distribution, the variance of the ages is of 1.5844.

What is the mean and the variance of a discrete distribution?

  • The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
  • The variance is given the sum of the difference squared between each outcome and the mean, multiplied by it's respective probability.

In this problem, considering the distribution given in the table, the mean is given by:

[tex]E(x) = 13(0.09) + 14(0.22) + 15(0.25) + 16(0.28) + 17(0.15) + 18(0.02) = 15.39[/tex]

Hence, the variance is given as follows:

[tex]Var(x) = 0.09(13-15.39)^2 + 0.22(14-15.39)^2 + 0.25(15-15.39)^2 + 0.28(16-15.39)^2 + 0.15(17-15.39)^2 + 0.02(13-15.39)^2 = 1.5844[/tex]

More can be learned about discrete distributions at https://brainly.com/question/24855677

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