Mathematics College

Let X and Y be independent and identically distributed exponential random variables with rate λ.
Let U = X/Y and let V = XY . Find the joint desnity for (U, V ). Also find the marginal densities fU (u)
and fV (v).

Answers

Answer 1

The joint density for (U, V) is given by:

f(u,v) = fX/Y,XY(u,v) = fX(v/u) * fY(v/u) * |(v/u)|

                = λ^2 * v * e^(-λv/u) * |(v/u)|

The marginal density for U is given by:

fU(u) = ∫f(u,v)dv

        = ∫λ^2 * v * e^(-λv/u) * |(v/u)|dv

        = λ^2 * u * ∫ve^(-λv/u)dv

        = λ^2 * u * (-(u/λ)^2 * e^(-λv/u))|v=0 to v=∞

        = λ^2 * u * (-(u/λ)^2)

        = λ^3 * u^2

The marginal density for V is given by:

fV(v) = ∫f(u,v)du

       = ∫λ^2 * v * e^(-λv/u) * |(v/u)|du

       = λ * v * ∫e^(-λv/u) * |(v/u)|du

       = λ * v * (∫e^(-λv/u)du)|v=0 to v=∞

       = λ * v * (-(u/λ) * e^(-λv/u))|u=0 to u=∞

       = λ * v * (-1)

       = λ * v

Therefore, the joint density for (U, V) is

f(u,v) = λ^2 * v * e^(-λv/u) * |(v/u)|du.

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Related Questions

I'm stuck on this math problem. Please only answer if your 100% sure. ( Look at the picture for the problem) Will Mark Brainliest. ​

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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The area of a triangle is 18. The base is 6 inches. What is the height?

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Answer:

the hight of your triangle is six inches

Find the measurements of the numbered angles in each kite.

Answers

Answer:

∠1 = 90°

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Step-by-step explanation:

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Answers

Answer:

LQ: 7.5

UQ: 21

Step-by-step explanation:

After identifying the median, remove it and split the data into two halves.

The upper quartile is the median is the top set of data and the lower quartile is the median is the bottom set of data.

If you have two numbers in the middle, you add them and divide by two to find the median/ quartile

so

[tex]\frac{7+8}{2} =7.5[/tex]

[tex]\frac{21+21}{2} =21[/tex]

Answer:
LQ: 7.5
UQ: 21

please help i need to pass

Answers

5.0000001.0000000
+
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Asma was asked to compare the following two numbers.
A = 6.212 x 108 and B = 4.73 x 10
She says,
“6.212 is bigger than 4.73 so A is bigger than B."
Is Asma correct?
You must give a reason for your answer

Answers

Answer:

No

Step-by-step explanation:

6.212 x 10^8 = 621,200,000

4.73  x 10^9 = 4,730,000,000

Yes Asma is correct because,

Even if we round off both no. to the nearest whole number we get 6 and 5 respectively.
That’s how we can also know which no. is bigger. The bigger no. is 6.212 and if we solve the equation, we get the answers
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So A is bigger than B in the two aspects mentioned above.

Hope this helped and have a nice day : )

Question 1 of 22
Klay's lunch cost $6. This is $2 less than Ella's lunch cost. How much did
Ella's lunch cost? Select the correct solution method, using x to represent the
cost of Ella's lunch.
A.
NIX
= 6. Multiply both sides by 2. Ella's lunch cost $12.
B. 2x = 6. Divide both sides by 2. Ella's lunch cost $3.
C. x + 2 = 6. Subtract 2 from both sides. Ella's lunch cost $4.
O D. X-2 = 6. Add 2 to both sides. Ella's lunch cost $8.

Answers

Answer:

D

Step-by-step explanation:

Because it says Klay lunch cost is $2 less than Ella's.

==> Ella's - $2 = Klay's

==> x-2=6

plus both side by 2

so the answer is $8

Musichelp me out please

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Answer:

right arrow

Step-by-step explanation:

10 points if you solve this!!!

Answers

Answer:

x = 128

Step-by-step explanation:

Right angles are 90 degrees.  90 + 90 + 52 = 232. 360 (angles in a quadrilateral) - 232 = 128.

Answer:

ans is 128

Step-by-step explanation:

90+90+52+x=360(all sides of triangle is 360)

180+52+x=360

232+x=360

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x=128

What is the volume of the rectangular prism? A.6/9 B.8/9 C.8/27 D. 6/27

Answers

Answer:

the corrct answer is C

Step-by-step explanation:

got it correct

an adult and 5 children rent skates. it cost $4 per adult for skates and a total of $16.

Answers

Answer:

$2.40 per child

Step-by-step explanation:

Subtract.

16 - 4 = 12

Divide.

12/5= 2.4

Very simple mental math. Please try to learn this 4th-5th grade math, you will definitely use this in real life, and it's not a pain to learn.

The cost of 4 pounds of potatoes is $3.56. What is the constant of proportionality that relates the cost in dollars, y, to the number of pounds of potatoes, x? A $0.89 A $0.89 B $1.12 B $1.12 C $8.90 C $8.90 D $1.02

Answers

Answer:

A. $0.89

Step-by-step explanation:

To find the constant of proportionality, find the cost of one pound of potatoes

3.56/4

= 0.89

So, the constant of proportionality is $0.89

The correct answer is A. $0.89

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Answers

Answer:

The number is 4

Step-by-step explanation:

Let the number  = 'x'

Reciprocal of 'x' = 1/x

Reciprocal of 2 = 1/2

8 times the reciprocal of 'x' = [tex]8*\frac{1}{x}\\[/tex]

[tex]8*\frac{1}{x}= 4* \frac{1}{2}\\\\8*\frac{1}{x}= 2\\[/tex]

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Now divide both sides by 2

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x = 4

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Answers

Answer:

310 in²

Step-by-step explanation:

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L = 20 in

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Area = 20*7 = 140 in²

✔️Area of the medium rectangle = L*W

L = 20 - 2 = 18 in

W = 22 - (10 + 7) = 5 in

Area = 18*5 = 90 in²

✔️Area of the smaller rectangle = L*W

L = 8 in

W = 10 in

Area = 8*10 = 80 in²

✅Area of the figure = 140 + 90 + 80 = 310 in²

Find the sum of -3x^2-4x+3−3x 2−4x+3 and 2x^2-x+32x 2 −x+3.

Answers

Answer:

28x^2-10x+9

Step-by-step explanation:

28x^2-10x+9

One third is equivalent to what number over 12?

Answers

Answer:

4/12

Step-by-step explanation:

1/3=x/12

using the butterfly method you see that

12=3x

and when solved you get

x=4

giving you

4/12

Also multiply 1/3 by 4 on each side

One third is equivalent to 4 over 12.

What is the fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Let the unknown number be x.

Here, 1/3 = x/12

Multiply both the numerator and denominator of 1/3 by 4, we get

4/12

So, 4/12 = x/12

x=12

Therefore, the unknown number is 12.

To learn more about the fraction visit:

brainly.com/question/1301963.

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100 Pts! PLS HELP ASAP!!!

Find the lateral area of this cone.
Leave your answer in terms of 7.
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Answers

Answer:

I’m pretty sure it’s basexHeight

Step-by-step explanation:

But other than that... i don’t know

Please don’t report me... I’m sorry for the :( answer

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Step-by-step explanation:

What is the slope of the line that passes through the points (6, 2) and (4, 10)?
-4
-1/4
1/4
4

Answers

Answer:

A. -4 (should have negative sign.)

Step-by-step explanation:

Slope formula:

[tex]\sf \dfrac{Y_2-Y_1}{X_2-X_1}[/tex]

y2=10

y1=2

x2=4

x1=6

Solve.

[tex]\dfrac{10-2}{4-6}[/tex]

10-2=8

4-6=(-2)

Divide.

8÷(-2)=-4

So, the correct answer is -4.

your answer would be -4. I hope this helped

Find the area of a rectangle with length of p+3 and width of 3p-2

Answers

Answer:

Area of rectangle = length × breadth

= ( p+3) (3p - 2)

= 3p² -2p + 9p -6

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A bag with 6 marbles has 2 blue marbles, 1 red marble, and 3 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is
blue?
Write your answer as a fraction in simplest form.

Answers

1/3 I’m pretty sure. you have 6 in total, there’s two blue 2/6 = 1/3

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

There are 6 marbles total. Divide the number of blue marbles by the total amount of marbles.

[tex]\frac{2}{6}[/tex]

Simplify

[tex]\frac{1}{3}[/tex]

Find the area of the regular polygon. Round to the nearest tenth.

Answers

Answer:

i dint know sorry

Step-by-step explanation:

Question 4 of 10 Which expression is equivalent to (b^m)^m? A. b^n-m B. b^n+m C. b^n•m D. b^n/m​

Answers

Answer:

C

Step-by-step explanation:

help asap
IS
Find the value of x. Round to the
nearest tenth.
35
х
12
X=
= [ ?]

Answers

Answer:

x ≈ 17.14

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )

x × tan35° = 12 ( divide both sides by tan35° )

x = [tex]\frac{12}{tan35}[/tex] ≈ 17.14 ( to the nearest tenth )

help, easy math. will mark brainlist!!​

Answers

Answer:

It is the first one 1/3(p+45).

Answer:

choice 1) 1/3(p + 45)

Step-by-step explanation:

1/3p + 15 = 1/3(p + 45)

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Answers

um where’s the question?

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