Question

STAT 190 Let X and Y have the joint probability density function (PDF), f X,Y (x, y) = kx, 0 < x < 1, 0 < y < 1 - x^2,

= 0, elsewhere,

where k is a constant.

1) What is the value of k.

2)What is the marginal PDF of X.

3) What is the E(X^2 Y).

Answer #1

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...

Let X and Y have the joint probability density function f(x, y)
= ⎧⎪⎪ ⎨ ⎪⎪⎩ ke−y , if 0 ≤ x ≤ y < ∞, 0, otherwise. (a) (6pts)
Find k so that f(x, y) is a valid joint p.d.f. (b) (6pts) Find the
marginal p.d.f. fX(x) and fY (y). Are X and Y independent?

The joint probability density function (pdf) of X and Y is given
by
f(x, y) = cx^2 (1 − y), 0 < x ≤ 1, 0 < y ≤ 1, x + y ≤
1.
(a) Find the constant c.
(b) Calculate P(X ≤ 0.5).
(c) Calculate P(X ≤ Y)

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and
0<=y<=1.
a) Find k.
b) Find the joint cumulative density function of (X,Y)
c) Find the marginal pdf of X and Y.
d) Find Pr[Y<X2] and Pr[X+Y>0.5]

The joint probability density function (pdf) describing
proportions X and Y of two components in a chemical blend are given
by f(x, y) = 2, 0 < y < x ≤ 1.
(a) Find the marginal pdfs of X and Y.
(b) Find the probability that the combined proportion of these
two components is less than 0.5.
(c) Find the conditional probability density function of Y given
X = x. (d) Find E(Y | X = 0.8).

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 .

Let f(x, y) = c/x, 0 < y < x < 1 be the joint density
function of X and Y .
a) What is the value of c?
a) 1 b) 2 c) 1/2 d) 2/3 e) 3/2
b)what is the marginal probability density function of X?
a) x/2 b)1 c)1/x d)x e)2x
c)what is the marginal probability density function of Y ?
a) ln y b)−ln y c)1 d)y e)y2
d)what is E[X]?
a)1 b)2 c)4 d)1/2 e)1/4

Let X and Y be two continuous random variables with joint
probability density function
f(x,y) =
6x 0<y<1, 0<x<y,
0 otherwise.
a) Find the marginal density of Y .
b) Are X and Y independent?
c) Find the conditional density of X given Y = 1 /2

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)

Let X and Y have the joint PDF (i really just need g and
h if that makes it easier)
f(x) = { c(y + x^2) 0 < x < 1 and 0 < y < 1 ; 0
elsewhere
a) Find c such that this is a PDF.
b) What is P(X ≤ .4, Y ≤ .2) ?
C) Find the Marginal Distribution of X, f(x)
D) Find the Marginal Distribution of Y, f(y)
E) Are X and Y...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 14 minutes ago

asked 14 minutes ago

asked 16 minutes ago

asked 20 minutes ago

asked 24 minutes ago

asked 26 minutes ago

asked 29 minutes ago

asked 35 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago