Let X and Y be continuous random variables with joint pdf
f(x, y) = kxy^2 0 < x, 0 < y, x
+ y < 2
and 0 otherwise
1) Find P[X ≥ 1|Y ≤ 1.5]
2) Find P[X ≥ 0.5|Y ≤ 1]
let the continuous random variables X and Y have the joint
pdf:
f(x,y)=6x , 0<x<y<1
i) find the marginal pdf of X and Y respectively,
ii) the conditional pdf of Y given x, that is
fY|X(y|x),
iii) E(Y|x) and Corr(X,Y).
Let X and Y be two continuous random variables
with the joint probability density function of for 0 < x
< 2, 0 < y < 2, x + y < 1,where c is a
constant. (In all the following answers, you do NOT need to find
what the value of c is; just treat it as a number.)
(a) Write out the marginal distribution of Y.
(b) P(Y < 1/3) = ?
(c) P(X < 1.5, Y < 0.5)=...
The joint pdf of a two continuous random variables is given as
follows: ??,? (?, ?) = { ??? 0 < ? < 2, 0 < ? < 1 0
??ℎ?????? 1) Find c. 2) Find the marginal PDFs of ? and ?. Make
sure to write the ranges. Are these random variables independent?
3) Find ?(0 < ? < 1|0 < ? < 1) 4) What is ??|? (?|?).
Make sure to write the range of ?.
Let X and Y be independent Exponential random variables with
common mean 1.
Their joint pdf is f(x,y) = exp (-x-y) for x > 0 and y > 0
, f(x, y ) = 0 otherwise. (See "Independence" on page 349)
Let U = min(X, Y) and V = max (X, Y).
The joint pdf of U and V is f(u, v) = 2 exp (-u-v) for 0 < u
< v < infinity, f(u, v ) = 0 otherwise....
Let X be a continuous random variable with pdf: f(x) = ax^2 −
2ax, 0 ≤ x ≤ 2
(a) What should a be in order for this to be a legitimate
p.d.f?
(b) What is the distribution function (c.d.f.) for X?
(c) What is Pr(0 ≤ X < 1)? Pr(X > 0.5)? Pr(X > 3)?
(d) What is the 90th percentile value of this distribution?
(Note: If you do this problem correctly, you will end up with a
cubic...
The joint probability density function (PDF) of two random
variables (X,Y) is given by
???(?,?) = { 1, 0 ≤ ? ≤ 2,0 ≤ ? ≤ 1,2? ≤ ? 0, otherwise
1) Find the correlation coefficient ??? between the two random
variables X and Y
Find the probability P(Y>X/2).
help please asap
Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i)
Find the conditional means of X given Y, and Y given X. (ii) Find
the conditional variance of X given Y. (iii) Find the correlation
coefficient between X and Y.
6. Two continuous random variables X and Y have the joint
density that is equal to c(x + y) 2 inside the square 0 ≤ x ≤ 1, 0
≤ y ≤ 1 and vanishes everywhere else.
a) Find the value of c
b) Find the marginal density fX(x) and use it to
determine E(X) and V(X)
c) Find the marginal density fY(y) and use it to
determine E(Y) and V(Y)
d) Find the correlation ρ(X,Y)
e) Are X and...