Each time a component is tested, the trial is a success (S) orfailure (F). Suppose the

A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space along with the associated value of X.

Give three examples of Bernoulli rvs (other than those in the text).

Using the experiment in Example 3.3, define two more random variables and list the possible values of each.

Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on the digits. What are the possible values of X? Give three possible outcomes and their associated X values.

If the sample space S is an infinite set, does this necessar ily imply that any rv X defined from S will have an infinite set of possible values? If yes, say why. If no, give an example.

Starting at a fixed time, each car entering an intersection is observed to see whether it turns left (L), right (R), or goes straight ahead (A). The experiment terminates as soon as a car is observed to turn left. Let X = the number of cars observed. What are possible X values? List five outcomes and their associated X values.

For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. a. X = the number of unbroken eggs in a randomly chosen standard egg carton b. Y = the number of students on a class list for a particular course who are absent on the first day of classes c. U = the number of times a duffer has to swing at a golf ball before hitting it d. X = the length of a randomly selected rattlesnake e. Z = the sales tax percentage for a randomly selected amazon.com purchase f. Y = the pH of a randomly chosen soil sample g. X = the tension (psi) at which a randomly selected tennis racket has been strung h. X = the total number of times three tennis players must spin their rackets to obtain something other than UUU or DDD (to determine which two play next)

Each time a component is tested, the trial is a success (S) or failure (F). Suppose the component is tested repeatedly until a success occurs on three consecutive trials. Let Y denote the number of trials necessary to achieve this. List all outcomes corresponding to the five smallest possible values of Y, and state which Y value is associated with each one.

An individual named Claudius is located at the point 0 in the accompanying diagram. A2 B2 A3 0 B1 A1 B4 A4 B3 Using an appropriate randomization device (such as a tetrahedral die, one having four sides), Claudius first moves to one of the four locations B1, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius next returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one of the (new) adjacent points is determined by tossing an appropriate die or coin. a. Let X = the number of moves that Claudius makes before first returning to 0. What are possible values of X? Is X discrete or continuous? b. If moves are allowed also along the diagonal paths connecting 0 to A1, A2, A3, and A4, respectively, answer the questions in part (a).

The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables: a. T = the total number of pumps in use b. X = the difference between the numbers in use at stations 1 and 2 c. U = the maximum number of pumps in use at either station d. Z = the number of stations having exactly two pumps in use