Question

Let X and Y be random variables with joint pdf f(x, y) = 2 + x − y, for 0 <= x <= 1, 1 <= y <= 2.

(a) Find the probability that min(X, Y ) <= 1/2.

(b) Find the probability that X + √ Y >= 4/3.

Answer #1

1. Let (X,Y ) be a pair of random variables with joint pdf given
by f(x,y) = 1(0 < x < 1,0 < y < 1).
(a) Find P(X + Y ≤ 1).
(b) Find P(|X −Y|≤ 1/2).
(c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R.
(d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY
of Y .
(f) Find the conditional pdf f(x|y) of X|Y = y for 0...

19. Let X and Y be continuous random variables with joint pdf:
f(x, y) = x−y for 0 ≤ y ≤ 1 and 1 ≤ x ≤ 2. If U = XY and V = X/Y ,
calculate the joint pdf of U and V , fUV (u, v).

Suppose X and Y are continuous random variables with joint
pdf
f(x,y) = x + y, 0 < x< 1, 0 < y< 1. Let W =
max(X,Y). Find EW.

Let X and Y be random variables with the joint pdf
fX,Y(x,y) = 6x, 0 ≤ y ≤ 1−x, 0 ≤ x ≤1.
1. Are X and Y independent? Explain with a picture.
2. Find the marginal pdf fX(x).
3. Find P( Y < 1/8 | X = 1/2 )

Suppose X and Y are continuous random variables with joint pdf
f(x,y) = 2(x+y) if 0 < x < < y < 1 and 0 otherwise.
Find the marginal pdf of T if S=X and T = XY. Use the joint pdf of
S = X and T = XY.

Let
X & Y be two continuous random variables with joint pdf:
fXY(X,Y) = { 2 x+y =< 1, x >0, y>0
{ 0 otherwise
find Cov(X,Y) and ρX,Y

4. Let X and Y be random variables having joint probability
density function (pdf) f(x, y) = 4/7 (xy − y), 4 < x < 5 and
0 < y < 1
(a) Find the marginal density fY (y).
(b) Show that the marginal density, fY (y), integrates to 1
(i.e., it is a density.)
(c) Find fX|Y (x|y), the conditional density of X given Y =
y.
(d) Show that fX|Y (x|y) is actually a pdf (i.e., it integrates...

The continuous random variables X and Y have joint pdf f(x, y) =
cy2 + xy/3 0 ≤ x ≤ 2, 0 ≤ y ≤ 1 (a)
What is the value of c that makes this a proper pdf? (b) Find the
marginal distribution of X. (c) (4 points) Find the marginal
distribution of Y . (d) (3 points) Are X and Y independent? Show
your work to support your answer.

Suppose X and Y are jointed distributed random variables with
joint pdf f(x,y) given by
f(x,y) = 8xy 0<y<x<1
= 0 elsewhere
What is P(0<X<1/2 , 1/4<Y<1/2)

Let X and Y have the joint pdf f(x,y) = 6*(x^2)*y for 0 <= x
<= y and x + y <= 2.
What is the marginal pdf of X and Y?
What is P(Y < 1.1 | X = 0.6)?
Are X and Y dependent random variables?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 13 minutes ago

asked 19 minutes ago

asked 22 minutes ago

asked 29 minutes ago

asked 34 minutes ago

asked 42 minutes ago

asked 42 minutes ago

asked 51 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago