- #1

Addez123

- 199

- 21

- 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?