Question

In: Statistics and Probability

Number of Girls x ​P(x) 0 0.0040.004 1 0.0330.033 2 0.1180.118 3 0.2260.226 4 0.2540.254 5...

Number of

Girls x

​P(x)

0

0.0040.004

1

0.0330.033

2

0.1180.118

3

0.2260.226

4

0.2540.254

5

0.2250.225

6

0.1070.107

7

0.0290.029

8

0.004

Refer to the accompanying​ table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.

Solutions

Expert Solution

Mean = (E(X)) = 0 * 0.004 + 1 * 0.033 + 2 * 0.118 + 3 * 0.226 + 4 * 0.254 + 5 * 0.225 + 6 * 0.107 + 7 * 0.029 + 8 * 0.004 = 3.965

E(X^2) = 0^2 * 0.004 + 1^2 * 0.033 + 2^2 * 0.118 + 3^2 * 0.226 + 4^2 * 0.254 + 5^2 * 0.225 + 6^2 * 0.107 + 7^2 * 0.029 + 8^2 * 0.004 = 17.757

Variance = E(X^2) - (E(X))^2

               = 17.757 - (3.965)^2

               = 2.036

Standard deviation = = 1.427

orchestra answered 2 years ago
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