Question

prove total probability of joint density function of bivariate normal distrubution is 1

Answer #1

2.
The joint probability density function of X and Y is given
by
f(x,y) = (6/7)(x² + xy/2),
0 < x < 1, 0 < y < 2. f(x,y) =0
otherwise
a) Compute the marginal densities of X and Y. b) Are X and Y
independent. c) Compute the conditional density
function f(y|x) and check restrictions on function you derived d)
probability P{X+Y<1}

Consider the joint density function f (x, y) = 1 if 0<=
x<= 1; 0<=y<= 1. [0 elsewhere]
a) Obtain the probability density function of the v.a Z, where Z =
X^2.
b) Obtain the probability density function of v.a W, where W =
X*Y^2.
c) Obtain the joint density function of Z and W, that is, g (Z,
W)

The joint probability density function of the quantity X of
almonds and the
Y quantity of walnuts in a 1 lb can was
F(x,y)=(24xy.
0≤=x<=1,
0≤=y<=1,
x+y<=1 )
otherwise
If 1 lb of almonds costs the company $ 1.50, 1 lb of walnuts costs
$ 2.25 and 1 lb of peanuts cost $ .75, what will be the total cost
of the contents of a can?, what will be the cost expected
total?

a) The joint probability density function of the random
variables X, Y is given as
f(x,y) =
8xy
if 0≤y≤x≤1 , and 0
elsewhere.
Find the marginal probability density functions.
b) Find the expected values EX and
EY for the density function above
c) find Cov X,Y .

1. Suppose the random variables ?? and ?? have the joint
probability density function,
??(??,??) =(4?? + 2??) / 75 ?????? 0 < ?? < 3 ?????? 0 <
?? < ?? + 1
a) Determine the marginal probability density function of ??.
b) Determine the conditional probability of ?? given ?? = 2.
2. To estimate the average monthly rent for 1 bedroom apartments,
13 complexes were randomly selected in Orlando. The mean cost is
$970 with a...

Let X and Y be a random variables with the joint probability
density function fX,Y (x, y) = { e −x−y , 0 < x, y < ∞ 0,
otherwise } . a. Let W = max(X, Y ) Compute the probability density
function of W. b. Let U = min(X, Y ) Compute the probability
density function of U. c. Compute the probability density function
of X + Y .

The
joint probability density function for two continuous random
variables is:
f(y1,y2) = k(y1^2 + y2)
for 0 <= y2 <= 1-y1^2
Find the value of the constant k so that this makes f(y1,y2) a
valid joint probability density function.
Also compute (integration) P(Y2 >= Y1 + 1)

2.
2. The joint probability density function of X and Y is given
by
f(x,y) = (6/7)(x² + xy/2),
0 < x < 1, 0 < y < 2. f(x,y) =0
otherwise
a) Compute the marginal densities of X and Y. b) Are X and Y
independent. c) Compute the conditional density
function f(y|x) and check restrictions on function you derived d)
probability P{X+Y<1} [5+5+5+5 = 20]

Let X and Y be two continuous random variables with joint
probability density function
?(?, ?) = { ? 2 + ?? 3 0 ≤ ? ≤ 1, 0 ≤ ? ≤ 2 0 ??ℎ??????
Find ?(? + ? ≥ 1). Sketch the surface in the ? − ? plane.

Problem 4 The joint probability density
function of the random variables X, Y is given as
f(x,y)=8xy
if 0 ≤ y ≤ x ≤ 1, and 0 elsewhere.
Find the marginal probability density functions.
Problem 5 Find the expected values E
(X) and E (Y) for the density function given
in Problem 4.
Problem 7. Using information from problems 4
and 5, find
Cov(X,Y).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 12 minutes ago

asked 17 minutes ago

asked 17 minutes ago

asked 20 minutes ago

asked 23 minutes ago

asked 26 minutes ago

asked 35 minutes ago

asked 43 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 48 minutes ago