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3 years ago

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Let the joint pmf of X and Y be f(x,y)=1/4, (x,y)∈S={(0,0),(1,1),(1,−1),(2,0)}. (a) Are X and Y independent? (b) Calculate Cov(X

,Y) andrho. This exercise also illustrates the fact that dependent random variables can have a correlation coefficient of zero

1 answer:

MrMuchimi3 years ago

8 0

Answer:

rtdjhvjhfdtktcfyukch

Step-by-step explanation:

You might be interested in

Lisa is cutting a 14-inch piece of paper into 0.4-inch strips. How many strips of paper will she have when she is finished?

QveST [7]

35 pieces since 14/.4 is 35.

5 0

2 years ago

Read 2 more answers

8x^-9+(-3x^-3y-2)(5/x^6y-2)

DaniilM [7]

$8x^{-9}+(-3x^{-3}y^{-2})(\frac{5}{x^6y^{-2}})$

the first step is to deal with the negative exponents, which causes numbers to go to the other side of the fraction

8x^{-9}+(-3x^{-3}y^{-2})(\frac{5}{x^6y^{-2}})

goes to

$\frac{8}{x^9}+(\frac{-3}{x^3y^2})(\frac{5y^2}{x^6})$

now we can simplify the multiplied terms

$\frac{8}{x^9}+(\frac{-15}{x^9})$

Now that we have common bases, we can add the 2 fractions together to get

$\frac{-7}{x^9}$

8 0

2 years ago

Use the intersect method to solve the equation. 14x^3-53x^2+41x-4=-4x^3-x^2+1x+4

UNO [17]

Answer:

x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

Step-by-step explanation:

Solve for x over the real numbers:

14 x^3 - 53 x^2 + 41 x - 4 = -4 x^3 - x^2 + x + 4

Subtract -4 x^3 - x^2 + x + 4 from both sides:

18 x^3 - 52 x^2 + 40 x - 8 = 0

Factor constant terms from the left hand side:

2 (9 x^3 - 26 x^2 + 20 x - 4) = 0

Divide both sides by 2:

9 x^3 - 26 x^2 + 20 x - 4 = 0

Eliminate the quadratic term by substituting y = x - 26/27:

-4 + 20 (y + 26/27) - 26 (y + 26/27)^2 + 9 (y + 26/27)^3 = 0

Expand out terms of the left hand side:

9 y^3 - (136 y)/27 - 1780/2187 = 0

Divide both sides by 9:

y^3 - (136 y)/243 - 1780/19683 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-1780/19683 - 136/243 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 136/243) - (1780 z^3)/19683 + z^2 (3 λ^2 - (136 λ)/243) + λ^3 = 0

Substitute λ = 136/729 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - (1780 u)/19683 + 2515456/387420489 = 0

Find the positive solution to the quadratic equation:

u = (2 (445 + 27 i sqrt(591)))/19683

Substitute back for u = z^3:

z^3 = (2 (445 + 27 i sqrt(591)))/19683

Taking cube roots gives 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) times the third roots of unity:

z = 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = -1/27 (-2)^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = 1/27 (-1)^(2/3) 2^(1/3) (445 + 27 i sqrt(591))^(1/3)

Substitute each value of z into y = z + 136/(729 z):

y = (68 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 1/27 (2 (27 i sqrt(591) + 445))^(1/3) or y = (68 (-2)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) - 1/27 (-2)^(1/3) (27 i sqrt(591) + 445)^(1/3) or y = 1/27 (-1)^(2/3) (2 (27 i sqrt(591) + 445))^(1/3) - (68 (-1)^(1/3) 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3))

Bring each solution to a common denominator and simplify:

y = (2^(1/3) ((27 i sqrt(591) + 445)^(2/3) + 68 2^(1/3)))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = 1/27 2^(1/3) (-1/(445 + 27 i sqrt(591)))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3))

Substitute back for x = y + 26/27:

Answer: x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

5 0

2 years ago

Please tell me the anwer please asap

CaHeK987 [17]

Answer:

The equation is:

y = -15*x + 1200

and:

a = 120

b = 70

c = -1500

Step-by-step explanation:

This seems to be a linear relationship.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Here we know that our line passes through the points (60, 300) and (20, 900)

Then the slope of this line is:

a = (900 - 300)/(20 - 60) = 600/(-40) = -15

Then this line is something like:

y = -15*x + b

To find the value of b, we know that this line passes through the point (60, 300) then when x = 60, we have y = 300.

Replacing these values in the above equation we get:

300 = -15*60 + b

300 + 15*60 = b = 1200

Then:

y = -15*x + 1200.

Now that we have this equation, we can complete the table.

a is the value for y, when x = 72

Then we can replace x by 72 in the above equation:

a = -15*72 + 1200 = 120

a = 120

b is the value of x when y = 150, then we need to replace y by 150

150 = -15*b + 1200

150 - 1200 = -15*b

(150 - 1200)/-15 = b = 70

then:

b = 70

c is the value of y when x = 180, then we need to replace x by 180.

c = -15*180 + 1200

c = -1500

5 0

2 years ago

Find the Area of the irregular figular

choli [55]

<span>the first thing to do is to divide the irregular shape into regular shapes that you can recognize such as triangles, rectangles, circles, squares Then you can, find the area of the individual shapes and add them up

</span>

3 0

3 years ago