sillybuffalo
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- Joined
- Sep 18, 2013
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- 9
The random variable X has the probability density function given by:
for x > 1
and
for x < or equal to 1.
The question asks me to find the expectation of the power X^p, for every p that is a real number.
I know that the expectation of the function of a random variable is given by:
where g(x) = x^p, and f_x(x) = c/(x^4)
Using the limits of integration from 1 to infinity, I was able to find
E[X^p] = -3 / (p-3) for p < 3.
However, I am having difficulty solving the integral for p = 3 and p >3, because the integral does not converge.
What am I doing wrong here?
for x > 1
and
for x < or equal to 1.
The question asks me to find the expectation of the power X^p, for every p that is a real number.
I know that the expectation of the function of a random variable is given by:
where g(x) = x^p, and f_x(x) = c/(x^4)
Using the limits of integration from 1 to infinity, I was able to find
E[X^p] = -3 / (p-3) for p < 3.
However, I am having difficulty solving the integral for p = 3 and p >3, because the integral does not converge.
What am I doing wrong here?
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