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Ray Of Light [21]
2 years ago
12

From families with four children a family is chosen at random. Let X be the number of boys in the family. Calculate and sketch t

he distribution function of X. Assume that in a four-child family all gender distributions (for example, BBBB, BBBB, BBBB, BBBB, etc.) are equally probable.
Mathematics
1 answer:
alisha [4.7K]2 years ago
4 0

Solution :

Given :

X = the number of boys in a family of four children

Families having four children are chosen randomly.

The gender distribution in the four child family are equally probable.

Thus,

 X                P(X)                                          CDF

0             ^4C_0 (1/2)^{4}        = 1/16                     \frac{1}{16}

1               ^4C_1 (1/2)^{4}       = 1/4                       \frac{5}{16}

2                ^4C_2 (1/2)^{4}      = 3/8                      \frac{11}{16}

3                ^4C_3 (1/2)^{4}      = 1/4                       \frac{15}{16}

4                  ^4C_4 (1/2)^{4}    = 1/16                      1

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Answer:

I'm glad you asked!

Step-by-step explanation:

OK,let's simplify the number for a equivalent expression.

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Distribute:

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Combine Like Terms:

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Transforming a shape involves changing the size and/or the location of the shape.

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<h3>Rigid transformation</h3>

When a shape is transformed by a rigid transformation, then the image of the shape will be congruent to the original shape.

An example of a rigid transformation is a reflection over the x-axis; and the rule is:

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So, a rule that will take the triangle to a congruent triangle is (x,y) \to (x,-y)

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When a shape is transformed by a nonrigid transformation, then the image of the shape will not be congruent to the original shape, however the original shape and the transformed shape would be similar

An example of a nonrigid transformation is a dilation by a scale factor od 0.5; and the rule is:

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So, a rule that will take the triangle to a figure that is similar is (x,y) \to (0.5x,0.5y)

However, if the x and y coordinates of the shape are dilated by different scale factors, then the resulting shape would neither be similar nor be congruent to the original shape.

A rule that will take the triangle to a figure that is not similar or congruent is (x,y) \to (0.5x,2y).

Read more about transformation at:

brainly.com/question/4289712

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