marginal density, conditional density, and probability

hollysti

New member
Joined
May 12, 2007
Messages
22
I have some of this problem done, but I can't figure it all out, so I will post how I have tried to solve each part after I post the question. Thanks for the help!

If X is the amount of money (in dollars) that the salesperson spends on gasoline during the day and Y is the corresponding amount of money (in dollars) for which he or she is reimbursed, the joint density of these two random variables is given by
f(x,y) = { 1/25((20 - x) / x) for 10 < x < 20, x/2 <y < x
0 elsewhere.
Find a) the marginal density of X, b) the conditional density of Y given X = 12, and c) the probability that the salesperson will be reimbursed at least $8 when spending $12.

For a), I tried to find the integral from x/2 to x of f(x,y), but I ended up with [1/25(lnx - x)] evaluated from x/2 to x. There is a mistake there somewhere because I know the correct answer is supposed to be g(x) = (20 - x)/ 50 for 10<x <20.
For b), I used what I know the correct answer for a) was supposed to be and solved f(x,y) / g(x). I got 1/6 and I this is the correct answer.
For c), I tried to use the integral from 8 to 12 of f(x,y), but, again, I am not getting the right answer (which is 1/3).

Any help would be greatly appreciated!
 

royhaas

Full Member
Joined
Dec 14, 2005
Messages
832
a) Integrate out y.
 

hollysti

New member
Joined
May 12, 2007
Messages
22
for a) am I evaluating from x/2 to x? I am not sure how to reduce that to the answer... what am I missing?
 
Top