Chapter 8: Chapter 8

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If \(A\) and \(B\) are events of an experiment, then $$P(A \cap B)=P(A \mid B) \cdot P(B)=P(B \mid A) \cdot P(A)$$

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false. \(\int_{1}^{\infty} \frac{d x}{x(x+1)}<\infty\).

Two cards are drawn from a well-shuffled deck of 52 playing cards. Let \(X\) denote the number of aces drawn. Find \(P(X=2)\)

Determine whether the events \(A\) and \(B\) are independent. \(P(A)=.6, P(B)=.8, P(A \cap B)=.2\)

In a four-child family, what is the expected number of boys? (Assume that the probability of a boy being born is the same as the probability of a girl being born.)

The probability distribution of a random variable \(X\) is given. Compute the mean, variance, and standard deviation of \(X\). $$\begin{array}{lccccc}\hline x & -198 & -195 & -193 & -188 & -185 \\ \hline P(X=x) & .15 & .30 & .10 & .25 & .20 \\ \hline\end{array}$$

Based on past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy \(0,1,2,3\), or 4 DVDs. How many DVDs can a customer entering this store be expected to buy? $$ \begin{array}{lccccc} \hline \text { DVDs } & 0 & 1 & 2 & 3 & 4 \\ \hline \text { Probability } & .42 & .36 & .14 & .05 & .03 \\ \hline \end{array} $$

Give the range of values that the random variable \(X\) may assume and classify the random variable as finite discrete, infinite discrete, or continuous. \(X=\) The number of times a die is thrown until a 2 appears

Give the range of values that the random variable \(X\) may assume and classify the random variable as finite discrete, infinite discrete, or continuous. \(X=\) The number of defective watches in a sample of eight watches

If a sample of three batteries is selected from a lot of ten, of which two are defective, what is the expected number of defective batteries?