/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q6E Starting at a fixed time, each c... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A computer disk storage device has ten concentric tracks, numbered \({\rm{1,2,}}...{\rm{,10}}\) from outermost to innermost, and a single access arm. Let \({{\rm{p}}_{\rm{i}}}{\rm{ = }}\)the probability that any particular request for data will take the arm to track \({\rm{i(i = 1,}}....{\rm{,10)}}\). Assume that the tracks accessed in successive seeks are independent. Let \({\rm{X = }}\)the number of tracks over which the access arm passes during two successive requests (excluding the track that the arm has just left, so possible \({\rm{X}}\) values are \({\rm{x = 0,1,}}...{\rm{,9}}\)). Compute the \({\rm{pmf}}\) of \({\rm{X}}\). (Hint: \({\rm{P}}\) (the arm is now on track \({\rm{i}}\) and \({\rm{X = j}}\))\({\rm{ = P(X = j larm nowon i)}} \cdot {{\rm{p}}_{\rm{i}}}\). After the conditional probability is written in terms of \({{\rm{p}}_{\rm{1}}}{\rm{,}}...{\rm{,}}{{\rm{p}}_{{\rm{10}}}}\), by the law of total probability, the desired probability is obtained by summing over \({\rm{i}}\).)

a. In a Poisson process, what has to happen in both the time interval \({\rm{(0,t)}}\) and the interval \({\rm{(t,t + \Delta t)}}\) so that no events occur in the entire interval \({\rm{(0,t + \Delta t)}}\)? Use this and Assumptions \({\rm{1 - 3}}\) to write a relationship between \({{\rm{P}}_{\rm{0}}}{\rm{(t + \Delta t)}}\) and \({{\rm{P}}_{\rm{0}}}{\rm{(t)}}\)

b. Use the result of part (a) to write an expression for the difference \({{\rm{P}}_{\rm{0}}}{\rm{(t + \Delta t) - }}{{\rm{P}}_{\rm{0}}}{\rm{(t)}}\) Then divide by \({\rm{\Delta t}}\) and let to obtain an equation involving \({\rm{(d/dt)}}{{\rm{P}}_{\rm{0}}}{\rm{(t)}}\), the derivative of \({{\rm{P}}_{\rm{0}}}{\rm{(t)}}\)with respect to \({\rm{t}}\).

c. Verify that \({{\rm{P}}_{\rm{0}}}{\rm{(t) = }}{{\rm{e}}^{{\rm{ - \alpha t}}}}\)satisfies the equation of part (b).

d. It can be shown in a manner similar to parts (a) and (b) that the \({{\rm{P}}_{\rm{k}}}{\rm{(t)}}\)must satisfy the system of differential equations

\(\begin{array}{*{20}{c}}{\frac{{\rm{d}}}{{{\rm{dt}}}}{{\rm{P}}_{\rm{k}}}{\rm{(t) = \alpha }}{{\rm{P}}_{{\rm{k - 1}}}}{\rm{(t) - \alpha }}{{\rm{P}}_{\rm{k}}}{\rm{(t)}}}\\{{\rm{k = 1,2,3, \ldots }}}\end{array}\)

Verify that \({{\rm{P}}_{\rm{k}}}{\rm{(t) = }}{{\rm{e}}^{{\rm{ - \alpha t}}}}{{\rm{(\alpha t)}}^{\rm{k}}}{\rm{/k}}\) satisfies the system. (This is actually the only solution.)

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)

Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying table.

y

45

46

47

48

49

50

51

52

53

54

55

p(y)

.05

.10

.12

.14

.25

.17

.06

.05

.03

.02

.01

a. What is the probability that the flight will accommodateall ticketed passengers who show up?

b. What is the probability that not all ticketed passengerswho show up can be accommodated?

c. If you are the first person on the standby list (whichmeans you will be the first one to get on the plane ifthere are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? What is this probability if you are the third person on the standby list?

Who studies more? Researchers asked the students in a large first-year college class how many minutes they studied on a typical weeknight. The back-to-back stemplot displays the responses from random samples of 30women and 30 men from the class, rounded to the nearest 10minutes. Write a few sentences comparing the male and female distributions of study time.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.