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Chapter 3: Q6E (page 98)

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

Short Answer

Expert verified

The possible X values are 1,2,3,4, and so on i.e.\(X \in \left\{ {1,2,3,4, \ldots } \right\}\)

Sample space

X

L

1

AL

2

RAL

3

AARL

4

AARRL

5

Step by step solution

01

Given information

The random variable X is defined as the number of cars observed entering an intersection.

The experiment terminates as soon as a car turns left is been observed.

02

Determine the possible X values

The random variable X can only take on positive values:\(1,2,3,4, \ldots \)as X counts the number of cars observed.

Therefore, the random variable is defined by:

\(X = \left\{ {1,2,3,4, \ldots } \right\}\)

The random variable X takes infinite set of values in this experiment.

03

List five possible outcomes with their associated values of X.

Here, X is defined as the number of cars observed and it terminated when the car turns left.

The samplespace of the experimentis\(S = \left\{ {L,AL,RAL,AARL,AARRL} \right\}\).

Following table, represent the possible outcomes and their associated values of X.

Sample space

X

L

1

AL

2

RAL

3

AARL

4

AARRL

5

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Most popular questions from this chapter

Consider a deck consisting of seven cards, marked\({\rm{1,2, \ldots }}\),\({\rm{7}}\). Three of these cards are selected at random. Define an rv \({\rm{W}}\) by \({\rm{W = }}\) the sum of the resulting numbers, and compute the pmf of \({\rm{W}}\). Then compute \({\rm{\mu }}\) and\({{\rm{\sigma }}^{\rm{2}}}\). (Hint: Consider outcomes as unordered, so that \({\rm{(1,3,7)}}\) and \({\rm{(3,1,7)}}\) are not different outcomes. Then there are \({\rm{35}}\) outcomes, and they can be listed. (This type of rv actually arises in connection with a statistical procedure called Wilcoxon's rank-sum test, in which there is an \({\rm{x}}\) sample and a \({\rm{y}}\) sample and \({\rm{W}}\)is the sum of the ranks of the \({\rm{x}}\)'s in the combined sample)

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