Let X and Y be two random variables. Suppose that2of X=4, and2of Y=9.If we know that the two random variablesZ=2XY andW=X+Y are independent, findCov(X,Y) andrho(X,Y)

Cov(X, Y) = -1/3 and (X, Y) = -1/18.Given data:X and Y are two random variables, of X=4, of Y=9.Z=2X Y and W = X + Y are independentTo find:Cov(X, Y) and (X, Y)Solution:We know that:Cov(X, Y) = E(XY) - E(X)E(Y)(X, Y) = Cov(X, Y) / X YLet's find E(X), E(Y), E(XY)E(X) = E(W - Y) = E(W) - E(Y)E(W) = E(X + Y) = E(X) + E(Y)From this equation, E(X) = E(W)/2 ------- (1)Similarly, E(Y) = E(W)/2 ------- (2)To find E(XY), we will use the following equation: E(XY) = Cov(X, Y) + E(X)E(Y)Using equations (1) and (2) in the above equation: E(XY) = Cov(X, Y) + E(W)/4Now, we will use the independence of Z and W to find Cov(X, Y).Cov(X, Y) = Cov((W - Z)/2, (W + Z)/3)= 1/6[Cov(W, W) - Cov(W, Z) + Cov(Z, W) - Cov(Z, Z)]= 1/6[Var(W) - Var(Z)]Here,Var(W) = Var(X + Y) = Var(X) + Var(Y) [using independence]= 4 + 9 = 13Var(Z) = Var(2X - Y) = 4Var(X) + Var(Y) - 2 Cov(X, Y)= 4 + 9 - 2 Cov(X, Y)Now, putting these values in Cov(X, Y),Cov(X, Y) = -1/3Also,X = 2 and Y = 3(X, Y) = Cov(X, Y) / X Y= -1/18Hence, Cov(X, Y) = -1/3 and (X, Y) = -1/18.To know more about random variables visit:https://brainly.in/question/23723704#SPJ11

Mathematics High School

Let X and Y be two random variables. Suppose that σ2 of X=4, and σ2 of Y=9.
If we know that the two random variables Z=2X−Y and W=X+Y are independent, find Cov(X,Y) and rho(X,Y)

Answers

Answer 1

Cov(X, Y) = -1/3 and ρ(X, Y) = -1/18.

Given data:X and Y are two random variables,

σ² of X=4,σ² of Y=9.Z=2X − Y and W = X + Y are independent

To find:

Cov(X, Y) and ρ(X, Y)

Solution:

We know that:

Cov(X, Y) = E(XY) - E(X)E(Y)ρ(X, Y) = Cov(X, Y) / σX σY

Let's find E(X), E(Y), E(XY)E(X) = E(W - Y) = E(W) - E(Y)E(W) = E(X + Y) = E(X) + E(Y)

From this equation, E(X) = E(W)/2 ------- (1)

Similarly, E(Y) = E(W)/2 ------- (2)

To find E(XY), we will use the following equation:

E(XY) = Cov(X, Y) + E(X)E(Y)Using equations (1) and (2) in the above equation:

E(XY) = Cov(X, Y) + E(W)²/4

Now, we will use the independence of Z and W to find Cov(X, Y).Cov(X, Y) = Cov((W - Z)/2, (W + Z)/3)= 1/6[Cov(W, W) - Cov(W, Z) + Cov(Z, W) - Cov(Z, Z)]= 1/6[Var(W) - Var(Z)]

Here,Var(W) = Var(X + Y) = Var(X) + Var(Y) [using independence]= 4 + 9 = 13Var(Z) = Var(2X - Y) = 4Var(X) + Var(Y) - 2 Cov(X, Y)= 4 + 9 - 2 Cov(X, Y)

Now, putting these values in Cov(X, Y),Cov(X, Y) = -1/3

Also,σX = 2 and σY = 3ρ(X, Y) = Cov(X, Y) / σX σY= -1/18

Hence, Cov(X, Y) = -1/3 and ρ(X, Y) = -1/18.

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Related Questions

What is the answer. Please dont send me ‘links’. I seriously need help.

Answers

Answer:

Total Volume of composite figure = 635.2 cm³

Steps:

CV = h×3.14×(d/2)²

CV = 5×3.14(8/2)²

CV = 5×3.14(4)²

CV = 5×3.14×16

CV = 5×50.24

CV = 251.2 cm³

RV = h×w×l

RV = 4×8×12

RV = 4×96

RV = 384 cm³

TV = CV + RV

TV = 251.2 + 384

TV = 635.2 cm³

A woman bought bars
of truck soap for #200. If
a bar is #2.50 more expensive.
She could have bought 2 less.
how many bars did she buy?

Answers

Answer:

Step-by-step explanation:

200/2.50=80

44444444444444 help me ples

Answers

Answer:

Step-by-step explanation:

how do i find a formula for "1+3+5+7+......+(2n-1)

Answers

Answer:

Step-by-step explanation:

common difference d=3-1=2

first term a=1

an=a+(n-1)d

2n-1=1+(l-1)2

2n-1=1+2l-2

2n-1=2l-1

l=n

(i used l for number of terms)

number of terms=n

[tex]S_{n}=\frac{n}{2} (first ~term+last~term)\\=\frac{n}{2} (1+2n-1)\\=n^2[/tex]

These numbers tell how many books five different students read in the past six months. 8, 11, 15, 22, and 6 a) Create a different set of five pieces of data with a greater mean, but with at least two values less than the values in the set of data above. b) Create a different set of five pieces of data with a lower mean, but with at least two values greater than the values in the set of data above. How did you make it work? c) Create a different set of five pieces of data with a lower mean, but with a higher median than the original set.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Origibal data set

8, 11, 15, 22, 6

Rearranging The value :

x : 6, 8, 11, 15,22

Mean = Σx / n

n = sample size =5

Mean = (6+8+11+15+22) = 62

Mean = 62 / 5 = 12.4

Median = 1/2(n+1)th term

Median = 1/2(6)th term = 6/2 = 3rd term = 11

A.)

X = 4, 5, 15, 23, 19

MEAN = (4 +5 + 15 + 23 + 19) / 5 = 13.2

B.)

X = 2, 6, 5, 23, 34

Mean = (2+6+5+23+24) / 5

Mean = 60 / 2 = 12

C.)

X = 3, 7, 12, 21, 13

X = 3, 7, 12, 13, 21

Mean = (3+7+12+13+21) /5 = 11.2

Median = 1/2(6)th term = 6/2 = 3rd term = 12

AD is tangent to circle B at point C. What is the measure of BCA? O 40° O 50° O 90° O 180°

Answers

Answer:

Step-by-step explanation:

B is likely the center, I think. You can't do it otherwise.

The tangent and a radius of a circle meet at 90o

therefore the answer is 90.

All of this could be confirmed with a diagram.

4/5 divided by 2/7 in simplest form

Answers

Answer:

2 4/5

Step-by-step explanation:

4/5 divided by 2/7 is 2.8. 2.8 in the form of a fraction is 2 4/5.

The fraction 4/5 divided by 2/7 in the simplest form, is 14/5.

Given that, (4/5) divided by (2/7).

To divide fractions, multiply the first fraction by the reciprocal of the second fraction

Let a, b, c and d be real numbers. Divide a fraction (a/b) by another fraction (c/d), we can multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by swapping the numerator and denominator. So, the reciprocal of (c/d) is (d/c).

To divide (a/b) by (c/d), multiply the first fraction by the reciprocal of the second fraction:

(a/b) ÷ (c/d) = (a/b) x (d/c)

Multiplying the numerators and denominators:

(ad) / (bc)

Therefore, the result of (a/b) divided by (c/d) is (ad) / (bc).

To simplify this expression, and multiply the first fraction by the reciprocal of the second fraction:

(4/5) x (7/2)

Multiplying the numerators and denominators:

(4 x 7) / (5 x 2)

Simplifying the numerator and denominator:

28 / 10

To further simplify the fraction, and divide both the numerator and denominator by their greatest common divisor, which is 2:

28 ÷ 2 / 10 ÷ 2

This gives us:

14 / 5

Therefore, the fraction 4/5 divided by 2/7, in the simplest form, is 14/5.

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What is the measure of the other acute angle.....?

I really need to get this right plsss help me ❤️ I really need to get to an 90

Answers

the answer is 30°

EXPLAINATION:

since the angle is a right angle triangle one of it's angles is 90°, and all the angles of a triangle always add up to 180°

so, 90° + 60° + x = 180

150° + x = 180°

so x = 180° - 150° = 30°

hence, the other acute angle is 30°.

Compute the indicated quantity using the following data.

sin α = 15/17 where π/2< α < 3π/2
sin β= -4/5 where π < β < 3π/2

sin (α + β) =_________

Answers

Using trigonometric identity, sin(α + β) = -28/85.

To compute sin(α + β), we can use the trigonometric identity:

sin(α + β) = sin α cos β + cos α sin β

Given the values:

sin α = 15/17 (π/2 < α < 3π/2)

sin β = -4/5 (π < β < 3π/2)

To find sin α, we can use the Pythagorean identity:

cos α = ±√(1 - sin² α)

Since α is in the range π/2 < α < 3π/2, sin α is positive, so cos α will be negative.

sin α = 15/17

cos α = -√(1 - (15/17)²)

= -√(1 - 225/289)

= -√(64/289)

= -8/17

Now, we can substitute the values into the formula for sin(α + β):

sin(α + β) = (sin α cos β) + (cos α sin β)

= (15/17) * (-4/5) + (-8/17) * (-4/5)

= -60/85 + 32/85

= -28/85

Therefore, sin(α + β) = -28/85.

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A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphere that can be packed inside the cube shaped box? Give you answer rounded to the nearest whole cubic inch

Answers

Answer:

6283 in³

Step-by-step explanation:

The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.

Since the cardboard box is in the shape of a cube, its volume V = L³

So, L = ∛V

Since V = 12000 in³,

L = ∛(12000 in³)

L= 22.89 in

So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2

So, V = 4π(L/2)³/3

= 4πL³/8 × 3

= πL³/2 × 3

= πL³/6

= πV/6

= π12000/6

= 2000π

= 6283.19 in³

≅ 6283.2 in³

= 6283 in³ to the nearest whole cubic inch

I need help im struggling

Answers

Answer:

62.80

Step-by-step explanation:

I hope this helped you out!!

Answer:

62.8

Step-by-step explanation:

Circumference is 2pi*radius. 2*pi*10 = 20 * 3.14 = 62.8

An ounce is equal to about 28 g. If 1 g of soil contains 2.5 billion bacteria, how many bacteria are in 1 oz of soil?

Answers

Answer:

About 700 billion bacteria

Step-by-step explanation:

Given

[tex]1oz \approx 28g[/tex]

[tex]1g = 25\ billion\ bacteria[/tex]

Required

Number of bacteria in 1 oz

[tex]1g = 25\ billion\ bacteria[/tex]

Multiply both sides by 28

[tex]28 * 1g = 25\ billion\ bacteria * 28[/tex]

[tex]28g = 700\ billion\ bacteria[/tex]

Recall that

[tex]1oz \approx 28g[/tex]

This means:

[tex]1oz \approx 700\ billion\ bacteria[/tex]

14. The diagonals of square ABCD intersect at E. If AE = 2, find the perimeter of ABCD.

Answers

Answer:

B, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Diagonals of a square are congruent so AC= 4

using pythagorean theorem we can then do [tex]x^{2} +x^{2}[/tex]=[tex]4^{2}[/tex]

[tex]2x^{2} = 16\\x^{2} =8\\x=\sqrt{8} \\x=2\sqrt{2}[/tex]

Then for perimeter we times the [tex]2\sqrt{2}[/tex] by 4 and get

[tex]8\sqrt{2}[/tex]

Hope this helps and please mark brainliest!!

Obtain the five-number summary for the given data The test scores of 15 students are listed below. 40 46 50 55 58 61 64 69 74 79 85 86 90 94 95 40,51.50, 71.5, 85.5,95 40, 55, 69, 86,95 40, 51.50, 69,

Answers

The five-number summary for the given data is as follows: Minimum = 40, First Quartile = 51.5, Median = 69, Third Quartile = 86, Maximum = 95.

To obtain the five-number summary, we consider the minimum, first quartile, median, third quartile, and maximum values of the dataset.

Minimum: The smallest value in the dataset is 40.

First Quartile: The first quartile (Q1) is the median of the lower half of the dataset. To find Q1, we arrange the data in ascending order: 40, 46, 50, 55, 58, 61, 64, 69, 74, 79, 85, 86, 90, 94, 95. Since there are 15 data points, the median is the 8th value (69), which becomes the first quartile.

Median: The median is the middle value of the dataset. In this case, since we have an odd number of data points, the median is the 8th value (69).

Third Quartile: The third quartile (Q3) is the median of the upper half of the dataset. Again, using the ordered data, we find Q3 as the median of the values above the median (69). This gives us the third quartile of 86.

Maximum: The largest value in the dataset is 95.

Thus, the five-number summary for the given data is Minimum = 40, Q1 = 51.5, Median = 69, Q3 = 86, and Maximum = 95.

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Evaluate the expression 6 + 5 × 32 - 8.

43
11
6
91

(and its not 32 its just the 2 is suppose to be up)

(dont steal my points)

Answers

Answer:

Step-by-step explanation:

A is the answer

Answer:

Ima steal your points

Step-by-step explanation:

For this data set, the best measure of center is the
, and its value is

Answers

Answer:

median, 60

Step-by-step explanation:

Answer:

it is 60 my friend.

Step-by-step explanation:

Each unit on the grid represents 2 kilometers. Find thedistance between Gabe's house and the library?

Answers

Answer:

8km

Step-by-step explanation:

there are 4 unit between Gabe's house and the library so distance is 4×2=8km

What is the slope and y intercept of 4x + 2y = 6?
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Answers

Answer:

4x−2y=6 is 21

Step-by-step explanation:

Answer:

Y intercept=3

4(0)+2y=6

y=3

slop=m=-2

y=-2x+3

y=mx+b

M=-2

Step-by-step explanation:

I don't know how to do this, I wasn't paying attention in class

Answers

Answer:

39.837168574084177751131265854635

Step-by-step explanation:

If you plug it into a calculator, you get that.

Next time, please pay attention in class and save us all a little trouble.

How many students choose strawberry kiwi

Need help with the answer please

NO LINKS!!!

Answers

Answer:

15 students. 30%

Step-by-step explanation:

explain why a divergent infinite series such as [infinity]x n=1 1 n can have a finite sum in floating-point arith- metic. at what point will the partial sums cease to change?

Answers

The partial sums will cease to change when the terms of the series become smaller than the smallest representable number in the floating-point system.

In floating-point arithmetic, there is a finite range of representable numbers and a limited precision for calculations. When dealing with infinite series, the terms are added or subtracted sequentially, but due to the limitations of numerical precision, there is a point at which the terms become too small to affect the sum significantly.

For the series 1/n, as n increases, the terms approach zero but never actually reach zero. Eventually, the terms become smaller than the smallest representable number in the floating-point system, and at this point, they essentially contribute zero to the sum. As a result, the partial sums of the series will cease to change beyond this point.

It's important to note that although the sum of the series may appear to be finite in floating-point arithmetic, mathematically, the series diverges and does not have a finite sum. The convergence to a finite value in floating-point arithmetic is a result of the limitations of numerical representation and precision. A divergent infinite series, such as the sum of 1/n from n=1 to infinity, can have a finite sum in floating-point arithmetic due to the limitations of numerical precision.

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Solve the initial value problem. dy dx Ex4(y – 2), y(0) = 6

Answers

This equation represents the solution to the given initial value problem.

[tex]1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}[/tex]

To solve the initial value problem, we'll separate variables and integrate both sides.

Starting with the given differential equation:

[tex]dy/dx = e^{4(y - 2)}[/tex]

Separating variables:

[tex]e^{(4(y - 2))} dy = dx[/tex]

Integrating both sides:

[tex]\int e^{(4(y - 2))} dy = \int dx[/tex]

To integrate [tex]e^{4(y - 2)}[/tex], we can use the substitution u = 4(y - 2), du = 4dy:

[tex]1/4 \int e^u du = x + C[/tex]

Integrating [tex]e^u[/tex] gives us:

[tex]1/4 * e^u = x + C[/tex]

Substituting back u = 4(y - 2):

[tex]1/4 * e^{(4(y - 2))} = x + C[/tex]

Now, applying the initial condition y(0) = 6, we can solve for C:

[tex]1/4 * e^{(4(6 - 2))} = 0 + C[/tex]

[tex]1/4 * e^{(4(4))} = C[/tex]

[tex]1/4 * e^{(16)} = C[/tex]

Therefore, the solution to the initial value problem is:

[tex]1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}[/tex]

This equation represents the solution to the given initial value problem.

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Is the cost of candy proportional to pounds of candy?

Answers

Answer:

Step-by-step explanation:

Yes

Answer:

yes because for every pound it is $3

Step-by-step explanation:

i know this because 1 times 3 is 3 and 3 times 3 is 9 and 7 times 3 is 21 and 10 times 3 is 30

Solve the system of equations using the substitution method.
x-4-5
2x + 3y - 23
Write your solution as an ordered pair:(

Answers

Answer:

(7, 3 )

Step-by-step explanation:

Given the 2 equations

x = 4y - 5 → (1)

2x + 3y = 23 → (2)

Substitute x = 4y - 5 into (2)

2(4y - 5) + 3y = 23 , that is

8y - 10 + 3y = 23

11y - 10 = 23 ( add 10 to both sides )

11y = 33 ( divide both sides by 11 )

y = 3

Substitute y = 3 into (1) for corresponding value of x

x = 4(3) - 5 = 12 - 5 = 7

solution is (7, 3 )

assume that the weight loss for the first month of a diet program varies between 6 and 12 pounds

Answers

The probability of the weight loss falling between 8 pounds and 11 pounds is 1/2

Variation of weight = Between 6 to 12.

It is required to ascertain the percentage of the overall range that corresponds to that interval in order to calculate the chance that the weight reduction will fall between 8 pounds and 11 pounds.

Calculating the total range of weight -

Range = Higher weight - Lower weight

= 12 - 6

= 6

Similarly, calculating the total range of weight for 8 pounds and 11 pounds

Range = Higher weight - Lower weight

= 11 - 8

Calculating the probability -

Probability = Range of interest / Total range

= 3 / 6

= 1/2.

Answers

It -3 correct answer

Answer:

-3

Step-by-step explanation:

The answer is -3 because it is the number on the x-axis

could someone help me with this

Answers

The answer is:

5.7•10^-3

Ava makes bead necklaces. She has a total of 6048 beads. Each necklace has 24 beads. Her friend maria says that the greatest number of necklace she can make with the beads is 162. Marias. Work is shown here

Answers

The question is incomplete:

Answer:

Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.

Step-by-step explanation:

You can find the number of necklaces Avan can make by dividing the number of beads she has by the amount in each necklace:

6048/24=252

According to this, you can say that Maria is incorrect because when you divide the number of beads by the beads in each necklace, you find that she can make 252 necklaces.

Which is greats 1,200 mm or 12 m

Answers

Answer:

12m

Step-by-step explanation:

1m = 1000mm

12m to mm

12 × 1000

= 12000mm

1200mm to m

1200 ÷ 1000

= 1.2m

What is the slope of the line through (-7,-2) and (−6,7)?

Answers

Answer:

slope = 9

Step-by-step explanation:

To find the slope of a line that passes through a pair of points, use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (-7,-2) and (-6,7) into the formula and simplify:

[tex]m = \frac{(7)-(-2)}{(-6)-(-7)} \\m = \frac{7+2}{-6+7} \\m = \frac{9}{1} \\m = 9[/tex]

So, the slope is 9.

Other Questions

Which event is less likely to occur:Event A: The product of the numbers 2 dice land on being less than 11. (Hint: theproduct is when you multiply 2 numbers together).Event B: Selecting a number at random from 1-30, inclusive, which has at least onedigit being 2. A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions? Classify the triangle as acute, obtuse, or right based on the given sidelengths. *8, 17, 19AcuteObtuseRight Assume that r* = 1.0%; the maturity risk premium is found as MRP = 0.1%(t - 1) where t = years to maturity; the default risk premium for Corporate bonds is found as DRP = 0.06% (t - 1); the liquidity premium is 0.80% for corporate bonds; and inflation is expected to be 4%, 5%, and 6% during the next three years and then 3% thereafter. What is the difference in interest rates between 10-year corporate bonds and 10-year Treasury bonds? do you think all seven steps of a sale are followed in every sale? why or why not? write down all prime numbers between 20 and 40 The United States became involved in World War II primarily because B) European democracies supported United States policies toward Germany and Japan B) European democracies supported United States policies toward Germany and Japan D) the Japanese empire bombed the US Naval base at Pearl Harbor, Hawaii D) the Japanese empire bombed the US Naval base at Pearl Harbor, Hawaii C) President Franklin D. Roosevelt did not enforce the Neutrality Acts C) President Franklin D. Roosevelt did not enforce the Neutrality Acts A) Germany refused to pay its debts from World War I A) Germany refused to pay its debts from World War I how much of a circle does a 100 degree angle turn through PART A: Which of the following statements best identifies a central idea of the article?A. The media attention on Mars enthusiasts has caused space exploration to become one of themost important issues facing Americans today.B. While some private agencies are working on sending humans to Mars, many experts believethat the barriers to such a voyage still remain high.C. Despite the publicity surrounding private space missions, NASA remains optimistic that itwill be the first agency in the U.S. to send humans to Mars.D. Private space agencies have no plans beyond landing on Mars, as opposed to the people ofNASA, who genuinely want to colonize Mars and explore space. Were any paint chip cards missing from your set? How did you determine they were or were not missing? How would you describe the missing cards to someone? On the dot below, which represents the book, draw and label the forces (not components) that act on the book at the lowest point of its circular path. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. ii. At the lowest point of the circular path, the book is moving only in the horizontal direction. In what direction, if any, is the net vertical force on the book? Up _No Down direction, since the net vertical force is equal to zero Without deriving any equations, briefly explain your reasoning in terms of the book's motion. write 9/6 as a mixed number Blue Llama Mining Company is analyzing a project that requires an initial investment of $600,000. The project's expected cash flows are Year Cash Flow Year $325,000 Year 2 -150,000 Year 3 475,000 Year 4500,000 Blue Llama Mining Company's WACC is 9%, and the project has the same risk as the firm's average project. Calculate this project's modified internal rate of return (MIRR): a) 14.91%. b) 18.64%. c) 19.57%. d) 20.50%. Let W1,W2W1,W2V be finite-dimensional subspaces of a vector space V. Showdim(W1+W2)=dimW1+dimW2dim(W1W2)dim(W1+W2)=dimW1+dimW2dim(W1W2)by successively addressing the following problems.(a) Prove the statement in the cases W1={0}W1={0} or W2={0}W2={0}.Hence, we may and will assume that W1,W2{0}W1,W2{0}. To this aim, we start from a basis of W1W2W1W2, which will later be completed to a basis of W1+W2W1+W2.(b) Let W1W2SW1W2 be a basis of W1W2W1W2. Show the existence of sets T1,T2T1,T2V such that T1ST1 is a basis of W1W1 and T2ST2 is a basis of W2W2.(c) Show that :=T1T2U:=ST1T2 spans W1+W2W1+W2.(d) Show that U is linearly independent, and deduce the claimed identity. If you borrow $500 for 6 years at an interest rate of 9%, how much interest will you pay? Bob had 42 fair tickets to sell. He sold 5/6 of the tickets. How many tickets did Bob sell A nurse is assessing a client who has a new diagnosis of diverticulitis and reports that he uses multiple complementary and alternative healing therapies. Which of the following complementary therapies should the nurse identify as contraindicated for the client? a. Acupuncture b. Colonics c. Guided imagery d. Saw palmetto Help me please Im not smart - pleaseeeee help i will pay you if u do and i really really need help on thisss!! its due tonight and i will fail if i dont get it done I need help with this.

Let X and Y be two random variables. Suppose that σ2 of X=4, and σ2 of Y=9. If we know that the two random variables Z=2X−Y and W=X+Y are independent, find Cov(X,Y) and rho(X,Y)

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Let X and Y be two random variables. Suppose that σ2 of X=4, and σ2 of Y=9.
If we know that the two random variables Z=2X−Y and W=X+Y are independent, find Cov(X,Y) and rho(X,Y)