# Probability density expected values

1. May 2, 2013

### afireinside

1. The problem statement, all variables and given/known data
Bearing capacity of soil varies between 6 and 15 kips/sq.ft. If probability density within this range is given as
f(x)=1/2.7 * (1- x/15), 6 ≤ u ≤ 15
=0 otherwise

Find E(X) and E(X^2)

2. Relevant equations
E(x) should be ∫x*f(x) dx
E(x^2) should be ∫x^2*f(x) dx

3. The attempt at a solution

E(x) ends up being 9 when I plug it in, but the answer sheet says either 9.55 or 9 * 55 (his decimals can look like multiplication dots)

E(x^2) ends up being 85.5, but the answer sheet says either 230.81 or 230 * 81.

I feel like it should be the * ones, because 9 and 81 are part of them, but I have no clue why, unless my equations are wrong.

2. May 2, 2013

### Simon Bridge

... what is "u" in there?
Do you mean:
$$f(x)=\frac{1}{2.7}\left (1-\frac{x}{15}\right )\; :\; 6\leq x \leq 16$$... then
$$E[X]=\frac{1}{243}\int_6^{15} (90x-6x^2)dx$$... sure enough - unless this is something funny in the course.

Probably you've just made a mistake someplace - or the answer sheet could be wrong.
Double check.

3. May 2, 2013

### afireinside

So are you saying the answer should be 9, and the answer sheet is wrong? Then what about E[x^2], is that 81 or is it 85.5 by doing a similar integral just with x^2 instead of x?

4. May 2, 2013

### Ray Vickson

I get EX = 9 and EX^2 = 85.5.

5. May 3, 2013

### Simon Bridge

Either the question is not what we think it is or the answer sheet is wrong.
I don't want to be definitive about this because I am not there and not the one doing the course.
You should check with someone else doing the course and ask the person who made the answer sheet.