Suppose f(x) = 0.125x for 0 < x < 4. determine the mean and variance of x. round your answers to 3 decimal places.

Answers

Answer 1

Answers:

- mean: 2.667
- variance: 0.889

Explanation:

To get the mean and variance of x, we need to verify first whether...
- x is discrete or continuous random variable
- f is probability mass or probability density function

because if we cannot verify the 2 statements above, we can't compute the mean and the variance.

Since 0 < x < 4, x is a continuous random variable because x can be any positive number less than, which includes a non-integer.

Note that if the random variable is continuous and [tex]0 \leq f(x) \leq 1[/tex] for any values of x in the domain of f, then f is a probability density function (PDF).

Note that

[tex]0 \ \textless \ x \ \textless \ 4 \\ \Leftrightarrow 0.125(0) \ \textless \ 0.125x \ \textless \ 0.125(4) \\ \Leftrightarrow 0 \ \textless \ 0.125x \ \textless \ 0.5 \\ \Leftrightarrow 0 \ \textless \ f(x) \ \textless \ 0.5 \\ \Rightarrow 0 \ \textless \ f(x) \ \textless \ 1 (\text{Because }0 \ \textless \ f(x) \ \textless \ 0.5 \ \textless \ 1)[/tex]

Hence, for any x in the domain of f, 0 < f(x) < 1. Moreover, since x is a continuous random variable, thus f is a PDF.

First, we use the following notations for mean and variance:

E[x] = mean of x
Var[x] = variance of x

Since f is a probability density function, we can use the following formulas for the mean and the variance of x:

[tex]\boxed{\text{mean of }x = E[x] = \int_{-\infty}^{\infty}{xf(x)}dx}[/tex]

[tex]\boxed{\text{Variance of }x = \text{Var}[x] = E[x^2] - (E[x])^2}} [/tex]

To compute for the mean of x,

[tex]\text{mean of }x = E[x] \\ = \int_{-\infty}^{\infty}{xf(x)}dx} \\ = \int_{-\infty}^{\infty}{x(0.125x)}dx} \\ \boxed{\text{mean of }x = \int_{-\infty}^{\infty}{0.125x^2}dx}}[/tex]

The integral seems complicated because of the infinity sign. But because the domain of f is the set of positive numbers less than 4, that is,

[tex]\text{domain of }f = \left \{x : 0 \ \textless \ x \ \textless \ 4 \right \}[/tex]

the bounds of the integral for the mean can be changed from [tex]-\infty \ \textless \ x \ \textless \ \infty[/tex] to [tex]0 \ \textless \ x \ \textless \ 4[/tex] so that

[tex]\boxed{\text{mean of }x = \int_{-\infty}^{\infty}{0.125x^2}dx = \int_{0}^{4}{0.125x^2}dx}[/tex]

Hence, the mean is computed as

[tex]\text{mean of }x = \int_{0}^{4}{0.125x^2}dx \\ = \left[ \frac{0.125x^3}{3} \right]_{0}^{4} \\ \\ = \left[ \frac{0.125(4)^3}{3} \right] - \left[ \frac{0.125(0)^3}{3} \right] \\ \\ \boxed{\text{mean of }x = \frac{8}{3} \approx 2.667} [/tex]

Since the formula for variance is computed as

[tex]\text{Variance of }x = \text{Var}[x] = E[x^2] - (E[x])^2[/tex]

we must first compute for [tex]E[x^2][/tex] for which

[tex]E[x^2] = \int_{-\infty}^{\infty}{x^2 f(x)}dx \\ \\ = \int_{-\infty}^{\infty}{x^2(0.125x)}dx \\ \\ \boxed{E[x^2] = \int_{-\infty}^{\infty}{0.125x^3}dx}[/tex]

Similar to the computation of integral of the mean, we take note that

[tex]\text{domain of }f = \left \{x : 0 \ \textless \ x \ \textless \ 4 \right \}[/tex]

so that we can change the bounds of the integral, that is,

[tex]\boxed{E[x^2] = \int_{-\infty}^{\infty}{0.125x^3}dx = \int_{0}^{4}{0.125x^3}dx}[/tex]

Hence,

[tex]E[x^2] = \int_{0}^{4}{0.125x^3}dx \\ \\ = \int_{0}^{4}{0.125x^3}dx \\ \\= \left[ \frac{0.125x^4}{4} \right]_{0}^{4} \\ \\ = \left[ \frac{0.125(4)^4}{4} \right] - \left[ \frac{0.125(0)^4}{4} \right] \\ \\ \boxed{E[x^2] = 8}[/tex]

Because [tex]E[x] = \frac{8}{3} [/tex],

[tex]\text{Variance of }x \\ \\ = E[x^2] - (E[x])^2 \\ \\ = 8 - \left( \frac{8}{3} \right)^2 \\ \\ \boxed{\text{Variance of }x = \frac{8}{9} \approx 0.889}[/tex]

Answer 2

Final answer:

The mean of x is 1.35 and the variance of x is approximately 1.267.

Explanation:

To find the mean of x, we need to calculate the expected value. We can do this by multiplying each value of x by its corresponding probability and then summing up the results. In this case, using the given values and probabilities, we have 0(0.20) + 1(0.45) + 2(0.20) + 3(0.10) + 4(0.05) = 1.35. Therefore, the mean of x is 1.35.

To find the variance of x, we need to calculate the squared difference between each value of x and the mean, weighted by their respective probabilities. We then sum up these values. Using the formula for variance, we have (0-1.35)²(0.20) + (1-1.35)²(0.45) + (2-1.35)²(0.20) + (3-1.35)²(0.10) + (4-1.35)²(0.05). By simplifying this expression, we find that the variance of x is approximately 1.267.

Learn more about Mean and Variance of x here:

https://brainly.com/question/33661677

#SPJ6

Related Questions

PLEASE HELP WILL GIVE BRAINLIEST!!!!!!! This is the graph of f(x). What is the value of f(2)?

Answers

the question answers are A 2 B 16 C 8 D 4

What is the area of this trapezoid? 96 in² 132 in² 168 in² 1344 in² Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 3 inches, F E is 8 inches., E C is 3 inches., E B is 12 inches., and A B is 8 inches.

Answers

Answer
132 〖in〗^2

Explanation
Although the diagram was not given, I was able to get it in the internet.
The area of a trapezium is found by the use of the following formula:
Area =1/2 h(a+b)
Where h is perpendicular distance between the two parallel lines, while a and b is are the lengths of the parallel lines.
In this question;
h=12 in
a=8 in
b=3+8+3=14 in
Area =1/2×12(8+14)
=6×22
132 〖in〗^2

Answer:

Option B. 132 inch²

Step-by-step explanation:

Since we know the formula to calculate the area of trapezoid is = [tex]\frac{1}{2}(height)(base)[/tex]

where height of the given trapezoid ABCD is side BE and two parallel sides are AB and DC.

It's given in the question

Side BE = 12 inches

AB = 8 inches

DC = (DF + FE + EC) = (3 + 8 + 3) = 14 inches

Now we put these values in the formula

Area of trapezoid ABCD = [tex]\frac{1}{2}(AB+CD).(BE) = \frac{1}{2}(8 + 14).(12)=\frac{1}{2}(22)(12)=(11).(12)=132[/tex]

Therefore answer is Option B. 132 inch²

A $65 coat is now on sale for $52. What percent discount is given?

Answers

20%
because if 65 is 100,
52 is 80% out of 65
so 100 - 80 is 20

The discount given is 20%! Hope this helps

Jan saw 9 full moons in 252 how do I write this in a ratio

Answers

9:252

Im sure the 252 means the days.

9:252 OR 9/252 There is the ratio and the proportion.

Simplify. 7 to the second power + 3 (-9-7) + 88 divides by 8 + 3 to the second power

Answers

Hello!

7[tex] x^{2} [/tex]+3 x - 16 + 88 ÷ 8 + [tex] 3^{2} [/tex]

49 + 3 x -16 + 88 ÷ 8 + [tex] 3^{2} [/tex]

49 + 3 x - 16 + 88 ÷ 8 + 9

49 - 48 + 88 ÷ 8 + 9

49 - 48 + 11 + 9

= 21
Your answer is 21.

Brainliest please?

20 PTS! What are the different shapes of a data set? Explain left and right skew and how this affects the mean of a data set.

Thanks, any help is much appreciated! :)

Answers

There are many shapes data sets could show. One example would be a symmetric data set. In this case both sides of the picture would look almost exactly or could be exactly (rarely) alike. In this case the mean could be used as a measure of center.

When the data is skewed right or left, the pictorial representation of the data will show less data points on the side where it is skewed and more data on the opposite side. The tail will be longer on the right if it is skewed right and vice versa.

In data that is skewed right, the mean will be greater than the median and if the data is skewed left, the mean will be less than the median. Tje mean is not the measure of center when the data is skewed.

A grain of sand has a mass of 2.6 × 10–3 gram. A grain of salt has a mass of 6.5 × 10–2 gram. How many times greater is the mass of the grain of salt than the mass of the grain of sand?

Answers

Let
x-----------> mass a grain of salt
y-----------> mass a grain of sand
r----------> ratio mass a grain of salt than mass a grain of sand

we know that
x=6.5 × 10–2 gram
y=2.6 × 10–3 gram
r=x/y----------> r=[6.5 × 10–2]/[2.6 × 10–3]----------> r=25

the answer is
the mass of the grain of salt is 25 times greater than the mass of the grain of sand

Answer:

the person above me is correct

Step-by-step explanation:

What is 0.125 Point rounded to the nearest hundredth

Answers

all you need to do is know what order (after decimals go in). Before the decimal you have, ones, tens, hundreds, etc. However, after the decimal you have tenths, hundredths. thousandths, etc. So the second value place is the hundredth place. You also have to round, so when you look at the 2( hundredths place) you look right one at the 5 (thousandths place) and see that it is somewhere from 5-9 so it makes the 2 a 3...so your answer is...

0.13

0.125 rounded to the nearest hundredth is 0.13.

We have,

To round to the nearest hundredth, we look at the digit in the thousandth place, which is 5.

Since 5 is greater than or equal to 5, we round up the hundredth digit (2) by increasing it by 1.

Therefore,

0.125 rounded to the nearest hundredth is 0.13.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

The number of miles that a commuter travels a car per day for one seven day work week is as follows: 19, 28, 17, 39, 22, 44, 56. The number of miles that a commuter travels on a bus per day for one seven day work week is as follows: 32, 26, 25, 40, 39, , 49, 22. Which method of transportation has a higher commuter average? Type either car or bus in the space provided. Use all lower case letters and do not use spaces in your answer.

Answers

car:
19 + 28 +17 +39 + 22 + 44 + 56 = 225
225/7 = 32.14

bus:
32 + 26 +25 + 40 + 39 + 49 + 22 = 233
233/7 = 33.29

the bus has the higher average

Mr,angelo sliced two pizzas into equal parts,what fraction greater than 1 names both pizzas

Answers

I really love pizza and would like to help you with this problem. So we have two pizzas. Maybe you like Neapolitan Pizzas, or Ham and Cheese Pizza, or Pepperoni Pizza, or Hawaiian Pizza. Anyway, no matter the type of pizza what is really important is that we can write the previous statement as follows:

[tex]Number \ of \ pizzas=2[/tex]

Each pizza is sliced as shown in the figure below, so we can write the new number of pizzas as follows:

[tex]Number \ of \ pizzas=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}[/tex]

But the problem is asking for a fraction greater than 1 to name both pizzas, then:

[tex]Number \ of \ pizzas=\frac{4}{2} \ or \ \frac{2}{1}[/tex]

A marker is randomly selected from a drawer that contains 20 green, 44 orange, and 30 blue markers.Which statement is true?

P(green)≈0.21P(blue)≈0.41P(orange)≈0.

Answers

[tex]Probability = \frac{number of choice}{total number of choices} [/tex]
# green = 20
# orange = 44
# blue = 30
Total = 20 + 44 + 30 = 94

[tex]P(green) = \frac{20}{94} = 0.212 [/tex]
[tex]P(orange) = \frac{44}{94} = 0.468[/tex]
[tex]P(blue) = \frac{30}{94} = 0.319[/tex]

The one that matches is A

Suppose 6 of 15 students in a grade-school class develop influenza where 20 percent of grade-school students nationwide develope influenza.

Answers

I am not sure what the question is here. I can tell you how to find the percent of kids that developed influenza in that class. We can compare it to the 20% of students nationwide. There could many different questions that stem from the piece of information you gave.

To find the percent of kids that developed influenza in that class do 6÷15 which gives you
.4 and written as a percent would be 40%.

Please message me if you have any questions! Hope this helps!

Which of the following statements contain a variable?all that apply
A.there are 60 second in a minute
B.he is year old
C.double the number of pages in the book
D.the age of my friend

Answers

B. and C.
Gotta write more for the 20 characters limit

CAN SOMEONE HELP PLZ AND EXPLAIN BEC IF DONT DO GOOD I CANT GO TO MY DADS HOUSE THIS WEEK END

Answers

Hello!

6.
Since the area is that of a square, you know that all side lengths are the same.

Area is base times height (A = bh), but since base and height are the same for a square, you get the formula A = a².

[tex]A = a^{2} [/tex]
[tex]144 = a^{2} [/tex]
[tex] \sqrt{144} = a[/tex]
[tex]12 = a[/tex]

The length of the side of a square with an area of 144 in² is 12 in.

7.
Rational number.

8.
This is a right triangle; use the Pythagorean Theorem to find missing lengths of right triangles. Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.

Plug in your leg lengths:

a² + b² = c²
8² + x² = 21²
64 + x² = 441
x² = 377
x = 19.4

you have a piggy bank containing a total of 93 coins in dimes and quarters. If the piggy bank contains $14.85, how many dimes are there in piggy bank

Answers

Let d = number of dimes.
Let q = number of quarters.

The total number of coins is 93, so the first equation is

d + q = 93

The value of 1 dime is $0.10. The value of 1 quarter is $0.25.
d dimes are worth 0.1d, and q quarters are worth 0.25q.
The total value of the coins is $14.85, so that gives us our second equation.

0.1d + 0.25q = 14.85

Now we have a system of two equations in two unknowns.

d + q = 93
0.1d + 0.25q = 14.85

Rewrite the first equation. Then multiply both sides of the second equation by -10, and write it underneath. Then add the equations.

d + q = 93
-d - 2.5q = -148.5
------------------------
-1.5q = -55.5

Divide both sides by -1.5.

q = 37

Now substitute 37 for q in the first original equation and solve for d.

d + q = 93

d + 37 = 93

Subtract 37 from both sides.

d = 56

Answer: There are 56 dimes in the piggy bank.

Which of the following are equivalent to 85%? 0.085, 0.85, 85/100, 19/20 ? chose all that apply?

Answers

.85 and 85/100 are the only ones within the question that are equivalent to 85%.

Add the sum of the numbers (−5.4) and (+8.2) to the opposite number of (−2 3/4 ).

Answers

The number are (−5.4) and (+8.2).
Sum of these two numbers are = (−5.4) + (+8.2)
= -5.4 + 8.2
= 2.8
Now we are going to add this to the opposite number of (−2 3/4 ).
(−2 3/4 ) = -11/4 = -2.75
now opposite number of -2.75 is 2.75
Thus,
2.8 + (2.75)
= 2.8 + 2.75
= 5.55

For a class gardening project, 1/3 of Mrs. Montoya's students planted marigolds and 1/2 planted tulips. What fraction of the class planted either marigolds or tulips?

Answers

Hi there!

To find the total fraction of the class that selected both marigolds and tulips, we need to add the two fractions together.

1/3 + 1/2 = 2/6 + 3/6

2/6 + 3/6 = 5/6

Hope this helps!

what is the probability of picking a vowel from the word invite?

Answers

6 total letters, 3 vowels. 3/6, or 1/2.

1/2 because there are 3 vowels out of all 6 letters. So, 3/6 converts to 1/2

The area of a rectangular barnyard is given by the trinomial 6x2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring. (1 point)

Answers

Area of a rectangular barnyard: A=6x^2+7x-20
A=6(6x^2+7x-20)/6
A=[(6^2)(x^2)+7(6x)-120]/6
A=[(6x)^2+7(6x)-120]/6
A=(6x+15)(6x-8)/6
A=(6x+15)(6x-8)/[(3)(2)]
A=(6x/3+15/3)(6x/2-8/2)
A=(2x+5)(3x-4)
A=bh
b=2x+5; h=3x-4
Answer: The possible dimensions of the barnyard are 2x+5 and 3x-4

Answer:

c 2x+5 and 3x-4

Step-by-step explanation:

The set of all points equidistant from the endpoints of a segment What term matches the definition? A) Central Angle Eliminate B) Perpendicular Bisector C) Segment D) Skew Lines

Answers

It is a perpendicular bisector.

Hope i helped :)

Mark wants a new car that costs $30,000. He only has $500 in his savings account and $300 in his checking account. Which financing option should he choose?

Answers

I would actually say that the best thing for Mark to do is to "Lease the car with a 0 percent down payment.". Sense he does not ave enough money to pay this car off, he would then have a better option to lease this car. By him doing this, it would help him to get to his destination faster and get things done for him.

Answer:

Mark should lease the car with 0% down payment.

Step-by-step explanation:

We know that the new car will cost = $30000.

Mark has only (500+300) = $800 with him.

That means Mark has only 2.66% of the cost of the car which is very less amount.

Thus Mark should have the car by leasing it with 0% down payment because in this way he will be able to buy or own the car with out giving any money for the car or without actually paying for the car and he can also at the same time can have his entire savings amount that he has as savings account and checking accounts.

Thus, he should lease the car with 0% down payment.

Chi needs to simplify the expression below.

Answers

she should need to do the subtraction in the parenthesis first

Subtraction. In order of operations, parenthesis comes first. Since the subtraction term is in the parenthesis, you would do that first. Then it's exponents, multiply, divide, add, and subtract. In the case that there are more than one multiplication/division operation, you would do it in the order from left to right. Same for subtraction/addition. Hope this adds a bit to your knowledge! Have a nice day :)

What is the greatest fraction you can make using the digits 4, 7, and 9?

Answers

Answer:

(7^9)/4 = 40,353,607/4

Step-by-step explanation:

Assuming each digit is used once and exponentiation is allowed, the largest numerator and smallest denominator will result in the largest fraction.

If other functions, such as factorial are allowed, then there might need to be a limit on the number of times they are applied. For example,

(7!)^(9!)/4 has about 1 million digits

something like ...

((7!)^(9!))!/4 has many more digits than that

and you can keep piling on the factorial symbols to any desired depth.

The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it. Always Sometimes Never

Answers

The ratio of the areas of two similar polygons can be found by squaring the ratio of their perimeters or corresponding linear dimensions, but this method only works sometimes, specifically with similar polygons, and not with non-similar ones.

The ratio of the areas of two similar polygons is indeed found by taking the ratio of their corresponding linear dimensions and squaring it. This is because the area is a two-dimensional measurement, whereas perimeter and linear dimensions are one-dimensional. For similar polygons, which are polygons that have the same shape but may have different sizes, any linear dimensions (such as sides, perimeters, diagonals) are proportional.

When you have two similar polygons and you know the ratio of their perimeters, you can use this perimeter ratio to find the ratio of their corresponding side lengths since the ratio of the perimeters of similar polygons is equal to the ratio of their corresponding linear dimensions. After finding this linear ratio, you square it to obtain the ratio of their areas because if one dimension is multiplied by a scale factor 's', the area is multiplied by 's' squared (scale factor squared).

It is important to note, however, that this rule only applies to similar polygons (similarity) and not to polygons that aren't similar, since non-similar polygons do not have a constant ratio of corresponding linear dimensions. Therefore, to answer the original question, the method works sometimes, specifically when dealing with similar polygons.

VWXY is a rhombus. find the measure

Answers

8. 6m-12
9. 6m-12+4m+4
10 is the same as above.
I'm not sure about 11.

I don't have access to a calculator. LOL

8)
rhombus, all sides are equal
so
6m - 12 = 4m+4
2m = 16
m = 8

VW = 6(8) - 12
VW = 48 - 12
VW = 36

XY = VW = 36

9)
3n^2 - 0.75 = 90
3n^2 = 90.75
n^2 = 30.25
n = 5.5

so
<YVW = 2(9*5.5 +4) = 2(53.5) = 107 degrees

10)
<VYX = 1/2(360 - 2*107)
<VYX = 1/2 (360 - 214)
<VYX = 1/2 (146)
<VYX = 73 degrees

11)
<XYZ = 1/2 (73) = 36.5 degrees

Marissa bought 2 1/2 gallons of orange juice to make punch.Marissa pours 1 1/2 cups of punch in each glass.How many fluid ounces is each serving

Answers

1.5 Times 8 =12 fl oz each serving
:)

1,600 principal earning 7%, compounded annually, after 33 years

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$1600\\ r=rate\to 7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &33 \end{cases} \\\\\\ A=1600\left(1+\frac{0.07}{1}\right)^{1\cdot 33}\implies A=1600(1.07)^{33}[/tex]

if you live 1 mile from work and can walk 4mph how long will it take you to get to work

Answers

4 miles = 1 hour
1 mile = 1/4 hour

1/4 hour = 15 mins

---------------------------------------------------------------------------------
Answer: It takes you 15 mins to walk to work
---------------------------------------------------------------------------------

solve this equation 12y=132

Answers

To solve this equation you have to find the value of y. Ask yourself "What times 12 can give me 132?"

132 / 12 = 11

12×11=132

y = 11

Other Questions

Mark and sally went walking in the park. both of them were wearing nothing on the upper half of their bodies. in american culture, mark would be violating a ________ and sally would be violating a ________. question 25 options: Which main groups supported Mussolinis effort to overthrow the government in Italy?union leaders, peasants, and businessmensoldiers, farm laborers, and factory workersarmy officers, wealthy landowners, and industrialistsnavy officers, wealthy politicians, and foreign officials, Find the number of inches needed to represent 300 miles if 1/4 in. = 50 mi. Where would the origin of endothermy map on the phylogeny? there was a young man from saint joe who excelled with his arrow and bow. hed take aim at the sun, and before he was done, the sun would lose half of its glow. use the poem to answer the questions. which form best describes this poem?A.narrativeB.concreteC.limerick D. haiku The early anthropologist who saw religion as rooted in a belief in spirits and the worship of them was The value of y directly varies with x, and y=5.4 when x =9. Find y when x= negative 10 According to erikson, a mother who __________ is likely to promote autonomy in toddlerhood. African American artists Kerry James Marshall says that works by people of color were only admitted into museums after they have been colonized and began making art like the Europeans .... true or false the graph below represents the price of Trisha chocolate chip cookies .How much would it cost to buy 30 of Trisha's cookies In 300 words or less, what was the key differences between Aristotles definitions of tragedy and comedy. How did the crusades change the economy of Europe Mucus occurs in both the respiratory and digestive tracts. what is its main immunological function? physically trapping of pathogens sweeping away debris destruction of pathogens because it is acidic increasing oxygen absorption A football stadium holds 52,000 fans. A college student is doing research and determines that on any given game day, the home team has five times as many fans as the visiting team. In order to help the student in his research, he represents the number of home team tickets as H and the visiting teams tickets as V. What strategy allowed the germans to achieve remarkable military success at the beginning of world war ii? between which two letters does differentiation occur? Which situation would be considered pseudoscience? Students gather to identify species of plants in their neighborhood. A students lucky necklace helps her win another volleyball tournament. Students are successful in petitioning for organic food in the cafeteria. A student tries eating all natural foods for one month to see if she has more energy. Example of figurative language the toast jumped out of the toaster. What effect of the argument can go with the example of figurative language A swing set is going to be placed over a region of mulch that is shaped like a trapezoid. The bases of the trapezoid have a length of 12 and 15 feet, and the perpendicular distance between the bases is 8.5 feet. What is the area of the region under the swing set? If necessary, round your answer to the nearest tenth. ENGLISH HELP!!In the beginning of the passage, the author writes The cherished objects we had brought with us thus far were left behind in the wagon, and with them, at last, our illusions.What illusions is the author most likely referring to?Question 2 options:Illusions of wealthIllusions of hopeIllusions of fameIllusions of war