integrating absolute values: For f(x) = 1 – |x|, -1 <= X <= 1, find E(X).

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__SB

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integrating absolute values: For f(x) = 1 – |x|, -1 <= X <= 1, find E(X).

f(x) = 1 – I x I -1 < X < 1 (less than or equal to)
Find E(x)
My question is why do you get
x(1 + x ) between the limits of -1 and 0 (integrating)
and x(1 – x) between 0 and +1
The rest of the question is not an issue; just unsure as towhy its 1 + x between those limits

Thanks in advance
 
__SB said:
f(x) = 1 – I x I -1 < X < 1 (less than or equal to)
Find E(x)
My question is why do you get
x(1 + x ) between the limits of -1 and 0 (integrating)
and x(1 – x) between 0 and +1
Click to expand...

\(\displaystyle |x|=\begin{cases}-x &: x< 0 \\ x &: x\ge 0\end{cases}\)
\(\displaystyle \displaystyle\int_{ - 1}^1 {\left( {1 - |x|} \right)dx} = \int_{ - 1}^0 {\left( {1 - [ - x]} \right)dx} + \int_0^1 {\left( {1 - [x]} \right)dx} \)
 
pka said:
\(\displaystyle |x|=\begin{cases}-x &: x< 0 \\ x &: x\ge 0\end{cases}\)
\(\displaystyle \displaystyle\int_{ - 1}^1 {\left( {1 - |x|} \right)dx} = \int_{ - 1}^0 {\left( {1 - [ - x]} \right)dx} + \int_0^1 {\left( {1 - [x]} \right)dx} \)
Click to expand...

Thanks for the response.
Why is mod x equal to –x when x < 0 ?
I always thought modulus just makes things positive?
 
__SB said:
Thanks for the response.
Why is mod x equal to –x when x < 0 ?
I always thought modulus just makes things positive?
Click to expand...
\(\displaystyle \Large |-3|=-(-3)=3\)
 
__SB said:
Thanks for the response.
Why is mod x equal to –x when x < 0 ?
I always thought modulus just makes things positive?
Click to expand...

Pka's response answers your question perfectly, but I just wanted to add that the absolute value function (i.e. |x|) and the modulus function (i.e. x % y) are not the same thing. Modulus is also sometimes called the remainder function, as it returns the remainder after division. That is to say,

6 % 3 = Remainder of 6 / 3 = 0
7 % 3 = Remainder of 7 / 3 = 1
8 % 3 = Remainder of 8 / 3 = 2
etc.
 
ksdhart2 said:
I just wanted to add that the absolute value function (i.e. |x|) and the modulus function (i.e. x % y) are not the same thing. Modulus is also sometimes called the remainder function, as it returns the remainder after division. That is to say,
Click to expand...
In most of the non-English speaking it is called the Modulus function.
I think that you are correct if it is spelled modulo function.
 
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