The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x. P(x) O 0.125 0.375 0.375 0.125 O A. mean: 1.50; standard deviation: 0.76 B. mean: 1.50; standard deviation: 0.87 O C. mean: 2.25; standard deviation: 0.76 O D. mean: 2.25; standard deviation: 0.87 x0123

Hi! Thank you for posting the question. Since you have posted multiple questions, we are answering first question. If you need help with any other question, please re-post the question and mention the part you need help with.

Let X represent the number of boys in a family.

Mean of the random variable X:

$\begin{array}{rcl}Mean& =& \sum _{}^{}xp\left(x\right)\\ & =& \left(0\right)\left(0.125\right)+\left(1\right)\left(0.375\right)+\left(2\right)\left(0.375\right)+\left(3\right)\left(0.125\right)\\ & =& 0+0.375+0.75+0.375\\ & =& 1.5\end{array}$