Chapter 16, Problem 16.1CRE

(a)

To determine

To check that the distribution of X satisfies the two requirements for a legitimate discrete probability model.

Explanation of Solution

Given:

The following are the birth order probabilities-

Calculation:

All probabilities are between $0$ and $1$ . The sum of probabilities is also $1$ and therefore account for all possible birth orders (9^th or higher birth order being included in the “8” group.

(b)

To determine

To find the probability $P(X\le 2)$ and $P(X\le 5)$ describing in the words.

Explanation of Solution

Given:

The following are the birth order probabilities-

Calculation:

  $P(X\le 2)$ Means the probability of baby’s birth order is less than or equal to $2$ .

  $P(X>5)$ Means the probability of baby’s birth order is greater than $5$

  $\begin{array}{l}P(X\le 2)=P(X=1)+P(X=2)\\ \Rightarrow P(X\le 2)=0.391+0.319\\ \Rightarrow P(X\le 2)=0.710\\ \\ P(X>5)=P(X=6)+P(X=7)+P(X=8)\\ \Rightarrow P(X>5)=0.012+0.005+0.005\\ \Rightarrow P(X>5)=0.022\end{array}$

(c)

To determine

To find out the probability of given event.

Explanation of Solution

Given:

The given event is-

The probability of event − “A woman gives birth in 2014 to her third child”.

Calculation:

The probability of event − “A woman gives birth in 2014 to her third child”.

  $P(X=3)=0.168$