 #1
 106
 11
 Homework Statement:

Into a cup with volume 'a' you pour volume X.
X has density function
$$fx(x) = (x+1)^{2}, x \geq 0$$
Y = volume in the cup after you've poured in X.
Calculate E(Y)
Note: if x > a then the cup flows over.
 Relevant Equations:
 $$E(Y) = \int g(x) * fx(x) dx, Y = g(x)$$
My guess is that g(x) = x?
The limits of integration should be 0 to a, since after a the cup flows over.
If I put these in, I get the solution (I've doubled checked with wolfram alpha that it's correct):
$$E(Y) = ln(a+1) + 1/(a+1)  1$$
The textbook solution is just ln(a+1).
I'm super new to the whole concept of probability so I'm just trying to make qualified guesses at what all the variables mean, obviously I did something wrong but what?
The limits of integration should be 0 to a, since after a the cup flows over.
If I put these in, I get the solution (I've doubled checked with wolfram alpha that it's correct):
$$E(Y) = ln(a+1) + 1/(a+1)  1$$
The textbook solution is just ln(a+1).
I'm super new to the whole concept of probability so I'm just trying to make qualified guesses at what all the variables mean, obviously I did something wrong but what?