Throughout this question
X and Y will be continuous random
variables which have joint probability density function
f
X;Y
( x, y) = c x y2 if 0 < y < x < 4 ;
= 0 otherwise
where c is some non-negative constant. Do the following:
(a) Determine the constant c. Answer =
15/
45 :
(b) Calculate the marginal density function
fY of Y . Answer =
15
2 (45) [ 16 y2 -y4 ] :
(c) Calculate
P [ 4 < X + Y ] . Answer =
59/
64
:
(d) Calculate
P [ Y < 2 j 4 < X + Y ] . Answer =
12/
59
:
(e) Calculate
P [ 2 < X j Y = 1 ] . Answer =
4/
5
Hey guys, this is a question on one of my tutorial sheets, Ive worked through the first 4 sucessfully but cant seem to get the correct answer for (e). We were given answers in class annd told to workout ourselves. Im just not sure am I doing it correctly. Here are the steps I took.
1: I drew the region on a graph, the x- values ran from x = 2 to x = 4 (for the purpose of integration limits) and the y values ran from y = 1 to y = x.
2: I found the joint density which I got to be 5772/6(45)
3: I worked out the value of the marginal density of y at y=1. And then divided this number into the joint density to get the conditional density.
Im just wondering where I have gone wrong and if anyone could give a helping hand
Thanks so much
Nappy