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Practice Problem: compute the zero-th order moment of a Gaussian random variable
A random variable X has the following probability density function:
$ f_X (x) = \frac{1}{\sqrt{2\pi} 3 } e^{\frac{-(x-3)^2}{18}} . $
Compute the moment of order zero of that random variable. In other words, compute
$ E \left( X^0 \right) . $
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
The moment of order n is defined as $ E(X^n)=\int_{-\infty}^{\infty} x^n*f_X(x) $
since $ x^0 = 1 $ and $ \int_{-\infty}^{\infty} f_X(x) = 1 $
the moment of order zero is $ E \left( X^0 \right) = 1 $
- Instructor's comment: Don't forget to put the "dx" in the integral. Also, I should warn you that the symbol "*" denotes convolution. I believe you mean "multiplication", right? Can anobody write a more "compact" solution? -pm
Answer 2
Write it here.
Answer 3
Write it here.
