# Binomial Distribution Parameter & Probability

A married couple decided to have $5$ children. Based on gene history, probability that any one of their children will need to wear eye glasses, independent of sex, is $60$%; probability that a child being a boy or a girl are equally $50$%. Let $X$ be the number of children that needs glasses and $Y$ be the number of boys in the family.

Probability distribution tables for $X$ and $Y$:

$$\begin{array}{} \begin{array}{c|c|c} \text{X} & \text{P(X)}\\ \hline \\0 & 0.01024 \\1 & 0.07680 \\2 & 0.23040 \\3 & 0.34560 \\4 & 0.25920 \\5 & 0.07776 \end{array} & \begin{array}{c|c|c} \text{Y} & \text{P(Y)}\\ \hline \\0 & 0.03125 \\1 & 0.15625 \\2 & 0.31250 \\3 & 0.31250 \\4 & 0.15625 \\5 & 0.03125 \end{array} \end{array}$$ Are the tables correct?

Both $X$ and $Y$ are binomial distributions. What are the parameter values?

What is $P(X=E(X))?$

Let $W$ be the number of girls that wear glasses. What is $P(W=E(W))?$

• Houston, we lost zero. – Did Feb 12 '13 at 19:29
• Zero is back, we happy. – Did Feb 13 '13 at 6:09