Chapter 5: Probability and Random Variables

What is the binomial distribution?

Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.

(a) If sampling is with replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.

(b) If sampling is without replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.

(c) If sampling is without replacement and the sample size does not exceed % of the population size, the probability distribution of the number of members sampled that have the specified attribute can be approximated by a distribution.

Give two examples of Bernoulli trials other than those presented in the text.

What does the "bi" in "binomial" signify?

Compute$3!,7!,8!,\mathrm{and}9!$.

Find$1!,2!,4!,\mathrm{and}6!$.

Evaluate the following binomial coefficients.

$\mathrm{a}.\left(\begin{array}{c}5\\ 2\end{array}\right)\mathrm{b}.\left(\begin{array}{c}7\\ 4\end{array}\right)\mathrm{c}.\left(\begin{array}{c}10\\ 3\end{array}\right)\mathrm{d}.\left(\begin{array}{c}12\\ 5\end{array}\right)$

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Preeclampsia. Preeclampsia is a medical condition characterized by high blood pressure and protein in the urine of a pregnant woman. It is a serious condition that can be life-threatening to the mother and child. In the article "Women's Experiences Preeclampsia: Australian Action on Preeclampsia Survey of Wom and Their Confidants" (Journal of Pregnancy,Vol. 2011, Issue 1, Article ID 375653), C. East et al. examined the experiences of 68 women with preeclampsia. The following table provides a frequency distribution of instances of prenatal or infant death for infants of women with preeclampsia.

Suppose that one of these women with preeclampsia is randomly selected. Find the probability that the child of the woman selected

(a) died.

(b). died one week to six months after birth.

(c). lived at least six weeks.

Evaluate the following binomial coefficients.

$\mathrm{a}.\left(\begin{array}{c}3\\ 2\end{array}\right)\mathrm{b}.\left(\begin{array}{c}6\\ 0\end{array}\right)\mathrm{c}.\left(\begin{array}{c}6\\ 6\end{array}\right)\mathrm{d}.\left(\begin{array}{c}7\\ 3\end{array}\right)$

Evaluate the following binomial coefficients.

$\mathrm{a}.\left(\begin{array}{c}4\\ 1\end{array}\right)\mathrm{b}.\left(\begin{array}{c}6\\ 2\end{array}\right)\mathrm{c}.\left(\begin{array}{c}8\\ 3\end{array}\right)\mathrm{d}.\left(\begin{array}{c}9\\ 6\end{array}\right)$