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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

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