The expected value of the assumed probability density function is 3/4 and the variance is 3/80
How to solve for E(x) and V(x)?The probability density function is not properly stated.
So, I will provide a general explanation on how to determine E(x) and V(x) of a probability density function
Assume that the probability density function is given as:
[tex]f(x)= \left[\begin{array}{ccc}3x^2 &0 \le x \le 1\\0&Otherwise\end{array}\right[/tex]
The expression E(x) is calculated using:
[tex]E(x) = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]
So, we have:
[tex]E(x) = \int\limits^1_0 {x \cdot 3x^2 \ d(x)[/tex]
Evaluate the product
[tex]E(x) = \int\limits^1_0 { 3x^3 \ d(x)[/tex]
Integrate
[tex]E(x) = \frac34x^4 |\limits^1_0[/tex]
Expand
[tex]E(x) = \frac34(1-0)^4[/tex]
Evaluate
[tex]E(x) = \frac34[/tex]
The variance is then calculated using:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Calculate [tex]E(x^2)[/tex] using:
[tex]E(x^2) = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]
This gives
[tex]E(x^2) = \int\limits^1_0 {x^2 \cdot 3x^2} \, dx[/tex]
Expand
[tex]E(x^2) = \int\limits^1_0 {3x^4} \, dx[/tex]
Integrate
[tex]E(x^2) = \frac{3}{5}x^5|\limits^1_0[/tex]
Expand
[tex]E(x^2) = \frac{3}{5}(1 - 0)^5[/tex]
Evaluate
[tex]E(x^2) = \frac{3}{5}[/tex]
Substitute [tex]E(x^2) = \frac{3}{5}[/tex] and [tex]E(x) = \frac34[/tex] in [tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = \frac 35 - (\frac{3}{4})^2[/tex]
Evaluate the exponent
[tex]Var(x) = \frac 35 - \frac{9}{16}[/tex]
Evaluate the difference
[tex]Var(x) = \frac{3}{80}[/tex]
Hence, the variance of the probability density function is 3/80
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Can someone help me with this question?
Answer: CD segment
Step-by-step explanation:
Anyone know what -8x-y=5 ; y=x+4 is using yhe subtraction method? Please explain to! would help greatly
Answer:
The answer would be x = -1 and y = 3
Step-by-step explanation:
Work is as shown:
1) -8x - y = 5
y = x + 4
2) -8x - (x+4) = 5
3) -8x -x = 9
4) -9x/-9 = 9/-9
5) y = -1 + 4 = 3
If there are any questions or if i didn't answer the question reply with the question please.
What is the product of the fraction below (3/x+2) (7/2x)
Answer:21x^2+14x over 2
Step-by-step explanation:
(2x)(2x)=(x+10)(2x-3) what is x?
Answer:
x = 5/2 or x = 6
Step-by-step explanation:
(2x)(2x)=(x+10)(2x-3)
4x^2 = 2x^2 - 3x + 20x - 30
2x^2 - 17x + 30 = 0
(2x - 5)(x - 6) = 0
x = 5/2 or x = 6
find the area of circle AOB 60 degrees and radius 7
Answer:
Solution: The radius of the circle is 7 inches and the angle is 60°. So, let us use the area of sector formula. The area of sector = (θ/360°) × π r2 = (60°/360°) × (22/7) × 72 = 77/3 = 25.67 square units.
Step-by-step explanation:
yan po ang sagot.
Find the mean of each distribution.
Correct answers will be mark as BRAINLIEST and get 50 points
Wrong answers will be reported
Answer:
See below ~
Step-by-step explanation:
a)
Mean = 3(21) + 1(22) + 2(23) + 5(24) + 1(25) / 12Mean = 63 + 22 + 46 + 120 + 25 / 12Mean = 276/12Mean = 23b)
Mean = 4.3 + 4.8 + 5.1 + 5.1 + 5.2 + 5.5 + 5.7 + 6.6 + 6.9 + 7.3 + 7.4 / 11Mean = 63.9/11Mean = 5.81Answer:
a) 23 °C
b) 5.81 m² (2 dp)
Step-by-step explanation:
Part (a)This set of data is presented as a Dot Plot.
The frequency (how often a data value occurs) is represented by the number of dots above each data value.
For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.
To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.
[tex]\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}[/tex]
Part (b)This set of data is presented as a stem and leaf diagram, where the units and tenths are split. The units column is the 'stem' and the tenths become the 'leaf'.
Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8
To find the mean, sum the data values, then divide by the total frequency.
To find the total frequency, simply count the number of values in the leaf part of the diagram.
Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4
Total frequency = 11
[tex]\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}[/tex]
Can someone help me with this
Answer:
95% = Within two standard deviations from the mean
99.7% = Within three standard deviations from the mean
68% = Within one standard deviation from the mean
Step-by-step explanation:
I hope this helped! If it did, please click "Thanks" to help me out!
Write down the next two terms in the sequence: 3, 15, 75 , ___, ___
answer pleass
I need it now
☹️
Answer:
375, 1875,
Step-by-step explanation:
hope this helps :)
Given x varies inversely as y and x = 6 when y = - 4, find y when x = 8 .
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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Given that x varies inversely with y, x=6 when y=-4, find y when x=8.
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
If x varies inversely with y, we divide.
So the formula looks as follows:-
[tex]\bold{x=\displaystyle\frac{k}{y} }[/tex]
where k = constant of proportionality
Plug in the values:-
[tex]\bold{6=\displaystyle\frac{k}{-4}}[/tex]
Multiply both sides by -4:-
[tex]\bold{-24=k}[/tex]
Now find y when x=8:-
[tex]\bold{8=\displaystyle\frac{-24}{y}}[/tex]
Multiply both sides by y:-
[tex]\bold{8y=-24}[/tex]
Divide by 8 on both sides:-
[tex]\dashrightarrow\bigstar{\boxed{\boxed{\underline{\bold{y=-3}}}}\dashleftarrow[/tex]
Good luck.
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please help me in this question please
Step-by-step explanation:
here is your answer, this is how you do it
Answer:
[tex]\boxed{\bf G. \: x = {25}^{o}} [/tex]
[tex]\boxed{\bf H. \: x = {20}^{o} }[/tex]
Step-by-step explanation:
In the given figure, the linear pairs are supplementary angles, meaning they should add up to 180°.
G)
[tex]\bf 2x + 34 + x + 71 = 18 {0}^{o} [/tex][tex]\bf 3x + 105 = 18 {0}^{o} [/tex][tex]\bf 3x = 180 - 105[/tex][tex]3x = 75[/tex][tex]\boxed{\bf x = {25}^{o} }[/tex]H)
[tex]\bf 2x + 4x + 3x = {180}^{o} [/tex][tex]\bf 9x = 180[/tex][tex]\boxed{\bf x = {20}^{o} }[/tex]«••••••••••••»«•••••••••••••»
Gravity is one of the four fundemental forces in the universe. Electromagnetism is another one. The Other two are the strong force and the weak force that happen at the subotamic level. Find some information on what role these two forces play inside each atom and why one is considered strong and the other weak
Answer:
gravity is the force that helps u stay on the earth
What is the range of the following numbers: 2, 5, 5, 8, 4, 3
Answer: range is 6
Step-by-step explanation:
Smallest number is 2
largest number is 8
8-2=6
Consider the solution to the system of inequalities below
-7x+y≥12.5
v+0.3x2 <-1
Which of the following functions could be added to the system without changing the solution set?
y < –2.1
y > –2.1
y = 2.1
y > 2.1
Answer:
i just want to try this but i think its y<2.1
Step-by-step explanation:
If for a particular one-to-one function f(2) = 13, what are the corresponding input and output
values for the inverse function?
Answer:
[tex]f^{-1}(13) = 2[/tex].
Step-by-step explanation:
For function [tex]f[/tex], the notation [tex]f(2) = 13[/tex] means that when the input to the function is [tex]2[/tex], the output would be [tex]13[/tex].
The inverse function of a one-to-one function [tex]f[/tex] is commonly denoted as [tex]\!f^{-1}[/tex].
The inverse function undoes the action of the original function. In this question, [tex]f[/tex] maps [tex]2[/tex] to [tex]13[/tex]. Thus, [tex]f^{-1}[/tex] would need to map [tex]13\![/tex] back to [tex]2\![/tex]. Therefore, [tex]f^{-1}(13) = 2[/tex] should be the corresponding input and output values.
x2 + y2 – 2y – 99 = 0
What is the center of this circle ?
],
What is the radius of this circle ?
units
Answer:
The center is at (h, k) : (0, -1) and the radius is 10. ... The radius is 10. That is, since r^2 = 100, r must be 10.
Step-by-step explanation:
hope this helps you!
What is the sum of 1/2plus 1/4use fractions strip to help
Answer:
Step-by-step e6/8 or in simple terms, 3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
1/2 is just 2/4
2/4+1/4 = 3/4
=)
Rachel bought a suit on sale for $268. This price was 33% less than the original price. What was the original price?
Answer:
$356.44
Step-by-step explanation:
Given the two similar flags shown,find the perimeter of the larger flag
The sum of the external side of a figure is its perimeter. the perimeter of the larger flag is 48
Similar shapesShapes are known to be similar if the ratioof their similar sides is equal to a constant.
From the given diagram, find the scale factor of the large triangle
k = 12/4
k = 3
Determine the perimeter of the large flag
Perimeter = 3 * perimeter of small flag
Perimeter of large flag = 3 * 16 = 48
Hence the perimeter of the larger flag is 48
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Find the area of the composite figure. First, find the area of the triangle.
Please help acellus sucks
Step-by-step explanation:
Rectangle area= 40×30= 1200cm²
Triangle area= 20×20= 400cm²
Total are of composite figure= 1200+400=1600cm²
Find the LCD of the rational expressions in the list
Answer:
30
Step-by-step explanation:
what number does 7 multiply by that also can be multiplied by 5? 30 is the least common denominator between 7 and 5.
Which statements are true about exponential functions? Check all that apply.
Answer:
The answer is A
Step-by-step explanation:
its a multiple answer choice. so A , D
9. Two fair dice are rolled. Find the odds of rolling the following sums.
(a) 2
(b) 6
(c) 9
(d) Between 5 and 8 (exclusive; that is, not including 5 or 8)
(e) Not more than 5
cedric's fish tank is 2yd long by 21in wide by 3ft tall. What is the volume of Cedric's take in cubic in?
Answer:
129 cubic inches
Step-by-step explanation:
lxwxh L=Length W=Width H= Height
Length times width times height gives you the volume
1. convert all numbers to inches
2. Multiply them together(order does not matter)
Solve the system using elimination.
Answer:
This equation has no solution
Step-by-step explanation:
if the same equation equals 2 different numbers then therefore there is no solution.
In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.
The function c(p) represents the cost for (P) people to attend the movies.
The function m(t) represents the miles driven over t hours.
The function t(m) represents the average high temperature for a given number of months.
The function p(w) represents the profit of a farmer who sells (w) whole watermelons.
The function (n) represents the number of person-hours it takes to assemble (n) engines in a factory.
Answer: The function c(p) represents the cost for (P) people to attend the movies.
The function t(m) represents the average high temperature for a given number of months.
Step-by-step explanation:
What is the value of the expression (8^2/3)^1/2
[tex]\left( 8^{\frac{2}{3}} \right)^{\frac{1}{2}}\implies \left( (2^3)^{\frac{2}{3}} \right)^{\frac{1}{2}}\implies 2^{3\cdot \frac{2}{3}\cdot \frac{1}{2}}\implies 2^{\frac{1}{1}}\implies 2[/tex]
2 7.1.2 Exam: Semester 1 Exam
Question 7 of 7
A part-time caregiver made $8944.58 last year. If he claimed himself as an
exemption for $3650 and had a $5700 standard deduction, what was his
taxable income last year?
O A. $5294.88
B. $3244.58
C. $0
O D. $405.42
Answer:$0
Step-by-step explanation:
Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service. a. What was her monthly income in the fi rst year after retirement?
Answer:
$1000
Explanation:
If the employee has worked there for 20 years and for every year its 50 dollars. That would mean its 50x20 which eqauls 1000.
The monthly income in the first year after retirement is $1000.
What is monthly income?Average monthly income is the amount you earn each month. Depending on your source of income, you can subtract insurance payments, rent allowances and other costs, such as federal and state taxes, from your total income every month. Net worth is your debt subtracted from your total assets.
Given that, Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service.
After working for 20 years, Janet has decided to retire from her job at a major department store.
The company has offered her a flat monthly retirement benefit of $50 for each year of service, which means that her monthly income in the first year after retirement would be $50 multiplied by 20, which is equal to $1000.
Hence, the monthly income in the first year after retirement is $1000.
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The height of a light pole in a magazine is 4 inches. The scale of the picture was given as 1 inch:24 inches. What would be the actual height of the light pole?
Answer:
96
Step-by-step explanation:
4 times 24 is 96
Which function has the greatest x-intercept?
Et
f(x) = 3x - 9
g(x) = (x + 31)
h(x) = 2x – 16
j(x) = -5(x - 2)2
Answer:
g(x) = (x + 31)
f(x)= 3x-9
3×x-9= -9+3×x
=-6x
g(x)=(x+31)
1×x+31=32+1×x
=32x
h(x)=2x-16
2×x-16= 16+2×x
=18x
j(x)= -5(x-2)2
(-5x+10)2
-10x+20= 10×x+20
=20-10×x
=10x