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 have the joint PDF
f(x) = { 1/2 0 < x + y < 2, x > 0, y > 0 ;
{ 0 elsewhere
a) sketch the support of X and Y
b) Are X and Y independent? Explain.
c) Find P(x<1 and y<1.5)
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.