Question

3.4. Determine if the3.4. Determine if the X and Y are statistically independent? Hint: (fx x y dx dy = 1)

Answer #1

Dear joint density is missing. But don't worry I will help you by explaining the concept of statistical independence.

Hope this will help you.. Dear if you have joint density please comment it.. I will help you...

Let X and Y be continuous random variables with joint density
function f(x,y) and marginal density functions fX(x) and fY(y)
respectively. Further, the support for both of these marginal
density functions is the interval (0,1).
Which of the following statements is always true? (Note there
may be more than one)
E[X^2Y^3]=(∫0 TO 1 x^2 dx)(∫0 TO 1 y^3dy)
E[X^2Y^3]=∫0 TO 1∫0 TO 1x^2y^3 f(x,y) dy dx
E[Y^3]=∫0 TO 1 y^3 fX(x) dx
E[XY]=(∫0 TO 1 x fX(x)...

Let X and Y be independent random variables with density functions given by fX (x) = 1/2, −1 ≤ x ≤ 1 and fY (y) = 1/2, 3 ≤ y ≤ 5. Find the density function of X-Y.

Let X and Y be independent positive random variables. Let Z=X/Y.
In what follows, all occurrences of x, y, z are assumed to be
positive numbers.
1. Suppose that X and Y are discrete, with known PMFs, pX and
pY. Then, pZ|Y(z|y)=pX(?). What is the argument in the place of the
question mark?
2. Suppose that X and Y are continuous, with known PDFs, fX and
fY. Provide a formula, analogous to the one in part (a), for
fZ|Y(z|y) in...

Question about using the convolution of distribution:
1. we have the formula: integral fx(x)fy(z-x)dx=integral
fx(z-x)fy(x)dx
I know this are equivalent. However, how do I decide which side
I should use ?
For example,X~Exp(1) and Y~Unif [0,1] X and Y independnt and the
textbook use fx(z-x)fy(x)dx.
However, can I use the left hand side fx(x)fy(z-x)dx???is there
any constraint for using left or right or actually both can lead me
to the right answer???
2. For X and Y are independent and...

Use implicit differentiation to determine dy/dx given the
equation e^x⋅y^3+x^4=sin(y)
dy/dx=

Solve: 1.dy/dx=(e^(y-x)).secy.(1+x^2),y(0)=0.
2.dy/dx=(1-x-y)/(x+y),y(0)=2 .

Calculate
dy
dx
.
Simplify your answer. HINT [See Examples 1 and 2.]
y =
3x − 5
2x + 4
dy
dx
=

Which of the following is an open sentence?
(z)((∼Yb ↔ Ya) ∨ (∃x)(Fx & Gx))
(y)((Cy ∨ (v)Dy) → ∼Yy)
((x)(Px & Myx) ↔ (y)(Cy ∨ Dy))

Let X and Y be two independent random variables. Given the
marginal pdfs indicated below, find the cdf of Y/X. (Hint: Consider
two cases, 0 ≤ w ≤ 1 and 1.) (a) fx (x) =1, 0 ≤ x ≤ 1, and fγ
(y)=1, 0 ≤ y ≤ 1 (b) fx (x)=2x,0 ≤x ≤1, and fy(y)=2y, 0 ≤y ≤1

Let X and Y be a random variables with the joint probability
density function fX,Y (x, y) = { cx2y, 0 < x2 < y < x for
x > 0 0, otherwise }. compute the marginal probability density
functions fX(x) and fY (y). Are the random variables X and Y
independent?.

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