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.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the mean
The formula for the mean $\mu$ of a discrete random variable is $\mu=\sum_{x}x\cdot P(x)$.
$$
\begin{align*}
\mu&=(0\times0.125)+(1\times0.375)+(2\times0.375)+(3\times0.125)\
&=0 + 0.375+0.75 + 0.375\
&=1.5
\end{align*}
$$
## Step2: Calculate the variance
The formula for the variance $\sigma^{2}$ is $\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)$.
$$
\begin{align*}
\sigma^{2}&=(0 - 1.5)^{2}\times0.125+(1 - 1.5)^{2}\times0.375+(2 - 1.5)^{2}\times0.375+(3 - 1.5)^{2}\times0.125\
&=(2.25\times0.125)+(0.25\times0.375)+(0.25\times0.375)+(2.25\times0.125)\
&=0.28125+0.09375 + 0.09375+0.28125\
&=0.75
\end{align*}
$$
## Step3: Calculate the standard deviation
The standard deviation $\sigma=\sqrt{\sigma^{2}}$.
$$
\sigma=\sqrt{0.75}\approx0.87
$$

# Answer:
A. mean: 1.50; standard deviation: 0.87

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the mean

Step2: Calculate the variance

Step3: Calculate the standard deviation

Answer: