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A couple decides to keep having children until they have a girl, at which point they will stop having children. They also agree to having a maximum of three children. The table below shows the probability distribution of X=, equals the number of children such a couple would have.
X=# of children 1 2 3
P(X), .5 .25 .25
Given that \mu_X=1.75μ
X
​
=1.75mu, start subscript, X, end subscript, equals, 1, point, 75 children, find the standard deviation of the children such a couple would have.
Round your answer to two decimal places.
\sigma_X\approxσ
X
​
≈sigma, start subscript, X, end subscript, approximately equals
children

Respuesta :

Answer:.83

Step-by-step explanation:

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From the discrete distribution given, the standard deviation is of 0.83 children.

The distribution is:

[tex]P(X = 1) = 0.5[/tex]

[tex]P(X = 2) = 0.25[/tex]

[tex]P(X = 3) = 0.25[/tex]

  • The mean is 1.75.
  • The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.

Hence:

[tex]\sqrt{V(X)} = \sqrt{0.5(1 - 1.75)^2 + 0.25(2 - 1.75)^2 + 0.25(3 - 1.75)^2} = 0.83[/tex]

The standard deviation is of 0.83 children.

A similar problem is given at https://brainly.com/question/24188569