A filtration process removes a random proportion of particulates in water to which it is applied. Suppose that a sample of water is subjected to this process twice. Let x1 be the proportion of the particulates that are removed by the first pass. Let X2 be the proportion of what remains after the first pass that is removed by the second pass. Assume that X1 and X2 are independent random variables with common pdf. f(x) = 4x3, for 0 < x <1 and f(x) = 0 otherwise. Let Y be the proportion of the original particulates that remain in the sample after two passes. Then Y = (1 - X1)(1 - X2). Find E(Y).
Answer:
[tex]E(Y)=\frac{1}{25}[/tex]
Step-by-step explanation:
Let's start defining the random variables for this exercise :
[tex]X_{1}:[/tex] '' The proportion of the particulates that are removed by the first pass ''
[tex]X_{2}:[/tex] '' The proportion of what remains after the first pass that is removed by the second pass ''
[tex]Y:[/tex] '' The proportion of the original particulates that remain in the sample after two passes ''
We know the relation between the random variables :
[tex]Y=(1-X_{1})(1-X_{2})[/tex]
We also assume that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] are independent random variables with common pdf.
The probability density function for both variables is [tex]f(x)=4x^{3}[/tex] for [tex]0<x<1[/tex] and [tex]f(x)=0[/tex] otherwise.
The first step to solve this exercise is to find the expected value for [tex]X_{1}[/tex] and [tex]X_{2}[/tex].
Because the variables have the same pdf we write :
[tex]E(X_{1})= E(X_{2})=E(X)[/tex]
Using the pdf to calculate the expected value we write :
[tex]E(X)=\int\limits^a_b {xf(x)} \, dx[/tex]
Where [tex]a=[/tex] ∞ and [tex]b=[/tex] - ∞ (because we integrate in the whole range of the random variable). In this case, we will integrate between [tex]0[/tex] and [tex]1[/tex] ⇒
Using the pdf we calculate the expected value :
[tex]E(X)=\int\limits^1_0 {x4x^{3}} \, dx=\int\limits^1_0 {4x^{4}} \, dx=\frac{4}{5}[/tex]
⇒ [tex]E(X)=E(X_{1})=E(X_{2})=\frac{4}{5}[/tex]
Now we need to use some expected value properties in the expression of [tex]Y[/tex] ⇒
[tex]Y=(1-X_{1})(1-X_{2})[/tex] ⇒
[tex]Y=1-X_{2}-X_{1}+X_{1}X_{2}[/tex]
Applying the expected value properties (linearity and expected value of a constant) ⇒
[tex]E(Y)=E(1)-E(X_{2})-E(X_{1})+E(X_{1}X_{2})[/tex]
Using that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] have the same expected value [tex]E(X)[/tex] and given that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] are independent random variables we can write [tex]E(X_{1}X_{2})=E(X_{1})E(X_{2})[/tex] ⇒
[tex]E(Y)=E(1)-E(X)-E(X)+E(X_{1})E(X_{2})[/tex] ⇒
[tex]E(Y)=E(1)-2E(X)+[E(X)]^{2}[/tex]
Using the value of [tex]E(X)[/tex] calculated :
[tex]E(Y)=1-2(\frac{4}{5})+(\frac{4}{5})^{2}=\frac{1}{25}[/tex]
[tex]E(Y)=\frac{1}{25}[/tex]
We find that the expected value of the variable [tex]Y[/tex] is [tex]E(Y)=\frac{1}{25}[/tex]
Which fraction is equivalent to 1/6
1/3
2/8
3/24
4/24
Answer:
the last one- 4/24
Step-by-step explanation:
ive answered this question before and got it correct
Then find the values of x and y?
Answer:
x=76
Step-by-step explanation:
y+8=3y
-2y=-8
y=4
104*2=208
360-208=152
152/2=76
x=76
Jim is twice as old as chin and four times as old as di.Their total ages altogether is equal to 84 years.Calculate jim's age
Answer:
48 years
Step-by-step explanation:
Let the ratio of their ages be
4:2:1
Sum up the numbers
4+2+1
= 7
Their total ages is 84
7/84
= 1/12
Therefore Jim age can be calculated as follows
= 12×4
= 48
Hence Jim is 48 years
Solve for 41.
1259
61 = [?]
61
37°
889
Answer: 55
Step-by-step explanation:
180 = 125 + x
x = 55
5y - 2y = 3y + 2
please help.
Multiplying polynomials
(4x+3y)(5x+y)
Answer:
20x^2 +19xy+3y^2
Step-by-step explanation:
See Image below :)
9514 1404 393
Answer:
20x² +19xy +3y²
Step-by-step explanation:
Use the distributive property.
(4x +3y)(5x +y)
= 4x(5x +y) +3y(5x +y)
= 20x² +4xy +15xy +3y²
Collect terms.
= 20x² +19xy +3y²
Angle Relationships
Determine the height of the triangle. Round to the nearest foot.
a. 12 ft
b. 14 ft
c. 10 ft
d. 18 ft
Please select the best answer from the choices provided
Answer:
B. 14 ft
Step-by-step explanation:
I calculated it logically
please help this is very important i will give you brain thing if its correct and no links pwease <3
Answer:
the 2nd and 3rd one I believe
Which is the simplified form of the expression?
10n−13(9n−12)
7n + 4
7n – 4
3n + 4
3n – 12
Given:
Consider the given expression is:
[tex]10n-\dfrac{1}{3}(9n-12)[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]10n-\dfrac{1}{3}(9n-12)[/tex]
Using distributive property, it can be written as:
[tex]=10n-\dfrac{1}{3}(9n)-\dfrac{1}{3}(-12)[/tex]
[tex]=10n-3n+4[/tex]
[tex]=7n+4[/tex]
Therefore, the correct option is A.
Selena's dog completed an obstacle course that was 452 meters long. There were four parts to the course, all equal length. How long was each part of the course?
Answer:
113 meters long
Step-by-step explanation:
If each part is all equal in length, then each part is 1/4 the total length of the obstacle course. Therefore, each part of the course was 1/4(452)=113 meters long
Need help please
What is the measure of angle 1?
What is the measure of angle 3?
What is the measure of angle 6?
Answer:
Step-by-step explanation:
Do you have any measurements?
1) 180-Angle 2 = Angle 1
3) Same as Angle 2
6) Same as Angle 2
No random links or answers, please.
Answer:
the ans is 21 hope it may help u
Step-by-step explanation:
g = 6
x=6
x= 3x + 3
x = 3 × 6 +3
x = 18 + 3
x= 21
PLEASE HELP WITH THIS ASPA 3/8 divided by-3/5
Answer:
Step-by-step explanation:
What is the volume of a sphere with a diameter of 49.3 cm, rounded to the nearest
tenth of a cubic centimeter?
Answer:
62739.3 cm3
Step-by-step explanation:
Volume of a Sphere:
V=43πr3V=\frac{4}{3}\pi r^3V=34πr3
radius=diameter2=49.32=24.65\text{radius} = \frac{\text{diameter}}{2} = \frac{49.3}{2}=24.65radius=2diameter=249.3=24.65
centimeters
Plug in:\text{Plug in:}Plug in:
43π(24.65)3\frac{4}{3}\pi (24.65)^334π(24.65)3
62739.258293562739.258293562739.2582935
Use calculator
≈62739.3 cm3\approx 62739.3\text{ cm}^3≈62739.3 cm3
Round to the nearest tenth
A rectangle is graphed on a coordinate plane. The rectangle’s two lines of symmetry are the x-axis and the y-axis. Evie says that means the vertices are reflections of each other over the x-axis and y-axis. Is she correct? Explain your reasoning NO LINKS worth 50 points
Answer:
Can you add a picture if there are any?
Step-by-step explanation:
A box of toy cars contains blue, orange, yellow, red, and black
cars. A separate box contains a male and a female action
figure. What is the probability of randomly choosing an orange
car and a female action figure? Is it likely or unlikely that this
combination is chosen?
Answer:
Step-by-step explanation:
A very weak university is on and off probationary status with the accrediting agency. A different procedure is used in July and in January to determine its status for the next 6 months. In July, the probability of changing status by coming off probation is .25; but the probability of changing status by going on probation is .12. In January, the probability of coming off probation is .15; but the probability of going on probation is .08. a) If the university is on probation as of February 2019; what is the probability it will be off probation in February 2020
Answer:
0.3425 = 34.25% probability it will be off probation in February 2020
Step-by-step explanation:
We have these desired outcomes:
Off probation in July 2019, with 0.25 probability, then continuing off in January, with 1 - 0.08 = 0.92 probability.
Still in probation in July 2019, with 1 - 0.25 = 0.75 probability, then coming off in January, with 0.15 probability.
What is the probability it will be off probation in February 2020?
[tex]p = 0.25*0.92 + 0.75*0.15 = 0.3425[/tex]
0.3425 = 34.25% probability it will be off probation in February 2020
What is the rule for the number pattern below ?950,800,650,500,350
Drag each solution to the correct location on the table. Each solution can be used more than once, but not all solutions will be used.
Determine the solutions to each of the given quadratic equations.
(3x + 8)(3x + 8) = 0
(3x-8)(3x + 8) = 0
x(3x - 8) = 0
(3x-8)(3x - 8) = 0
= -8
Answer:
The answers to your questions are given below.
Step-by-step explanation:
1. (3x + 8)(3x + 8) = 0
3x + 8 = 0 or 3x + 8 = 0
3x = –8 or 3x = –8
x = –8/3 or –8/3
2. (3x – 8)(3x + 8) = 0
3x – 8 = 0 or 3x + 8 = 0
3x = 8 or 3x = –8
x = 8/3 or –8/3
3. x(3x – 8) = 0
x = 0 or 3x – 8 = 0
x = 0 or 3x = 8
x = 0 or 8/3
4. (3x – 8)(3x – 8) = 0
3x – 8 = 0 or 3x – 8 = 0
3x = 8 or 3x = 8
x = 8/3 or 8/3
Simplify the expression using order of operation 5 x 2 + 3 to the power of 2
answer= 1
5 x 2 - 3^2
1. First simplify exponents
= that is nine
2. Then Do 5 x 2- 9
5 x 2=10
10-9
= 1
Simplify: x^1/3( x^1/2 + 2x^2)
Answer:
Step-by-step explanation:
x^1/3( x^1/2 + 2x^2)
x^(1/2 + 1/3) + 2x^(2 + 1/3)
x^(5/6) + 2x^(7/3)
What is the zero of function f?
f(x)=7^3Vx+12-12
Answer:
hope it helps ya.
please give me brainliest
Leroy wants to teach his puppy 6 new tricks. In how many different orders can the puppy learn the tricks?
Answer: 720 ways
Step-by-step explanation:
Given
Leroy wants to teach his puppy 6 new tricks
Considering each trick is different from other
The first trick can be taught in 6 different ways
After learning the first trick, there are 5 tricks remaining which can be taught in 5 different ways
Similarly, for the remaining tricks, it is 4, 3, 2, and 1 way
So, the total number of ways is [tex]6\times 5\times 4\times 3\times 2\times 1=720\ \text{Ways}[/tex]
Two planes start from the same point and fly opposite directions. The first plane is flying 20 mph slower than the second plane in 2 h the planes are 540 mi apart. Find the rate of each plane
Answer:
This
Step-by-step explanation:
let x = rate of the slower plane (First plane!)
x+25 = rate of the faster plane (Second plane!)
The planes fly for 2 hours, where Distance = R*T
Distance between the planes = SUM of the distances.
R*T + R*T= 470 miles
2*x + 2*(x+25)=470
2x+2x + 50 = 470
4x+50=470
4x=420
x=105 mph First plane
x+25= 105+25=130 mph Second plane.
Answer:
4x+50=470
4x=420
x=105 mph First plane
x+25= 105+25=130 mph Second plane.
R^2
Step-by-step explanation:
In triangle ABC, m
15
1353
25
Plz help me well mark brainliest if correct!!.....
Answer:
12 inches
Step-by-step explanation:
All you have to do is divide 72 by 6.
72 divided by 6 equals 12.
So your answer would be D.12 inches
Pls answer this. I need the answer quick. Just write the answer. no downloads
Answer:
POINTS HA
Step-by-step explanation:
The diameter of a dime is 17.91 millimeters, an the height is 1.35 millimeters. What is the volume of a dime? What is the volume of an oblique cylinder formed by stacking 50 dimes? Round your answers to the nearest hundredth.
Answer:
why does no one ever answer these questionsss?? it's always math to, like I'm just trying to pass my quick check, let alone the class. you know how much easier my life would be it's people just answered the questions. I'm gonna run away, to some Scottish Isle and live a quiet life, in a cozy home with the wind outside ruffling through the grass, and the tired tired sea crashing onto the shoreline. I'll only visit my family and friends once a year, but the rest of the time, I'll be there, in the quiet. eventually a young visitor will stumble through my b & b and he'll end up staying there for weeks, for reasons unknown to me. Then, we'll fall in love, to the quiet sound of the ocean outside. And it'll be just us, it'll be our place, our secret. we won't have to deal with the loud, crazy, hectic world. and it will be perfect. but for now I'm stuck trying to pass this math class.
Answer:
The volume of one dime is 340.11 mm3. The volume of 50 dimes is 17.005.32 mm3.
Step-by-step explanation:
Last year a farm produced 6.2 - 10^6soybeans and 7.8. 10^6 onions.
a.) What was the total number of vegetables produced by the farm last year?
Answer:
Yessir
Step-by-step explanation: