How can I find expected value with f(x) equaling multiple equations?

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teetar

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Dec 2, 2013
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Hello, I'm trying to finds the mean and median of X, X being defined as a continuous random variable with probability density function:

f(x) = k(x+2)^2 , -2≤x<0
f(x) = k , 0≤x≤4/3
f(x)= 0, otherwise
where k = 1/8

In order to find the mean/expected value, I understand I should have to take the definite integral of xf(x), but I don't know how that should work with these two definitions of f(x). I should take the integral between -2 and 0 of xk(x+2)2 and the integral between 0 and 4/3 of xk, but how do I relate these in order to get the expected value of X?

Thanks for any help, and sorry for my shoddy formatting, I've completely forgotten LaTeX.
 
teetar said:
Hello, I'm trying to finds the mean and median of X, X being defined as a continuous random variable with probability density function:

f(x) = k(x+2)^2 , -2≤x<0
f(x) = k , 0≤x≤4/3
f(x)= 0, otherwise
where k = 1/8

In order to find the mean/expected value, I understand I should have to take the definite integral of xf(x), but I don't know how that should work with these two definitions of f(x). I should take the integral between -2 and 0 of xk(x+2)2 and the integral between 0 and 4/3 of xk, but how do I relate these in order to get the expected value of X?

Thanks for any help, and sorry for my shoddy formatting, I've completely forgotten LaTeX.
Click to expand...

\(\displaystyle \int_a^b\, f(x)\, dx\) = \(\displaystyle \int_a^{c_1}\, f(x)\, dx\) + \(\displaystyle \int_{c_1}^{c_2}\, f(x)\, dx\) + \(\displaystyle \int_{c_2}^{c_3}\, f(x)\, dx\) + \(\displaystyle ...\, \int_{c_{n-1}}^{c_n}\, f(x)\, dx\) + \(\displaystyle \int_{c_n}^b\, f(x)\, dx\)
 
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