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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) . $


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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.


Back to ECE302 Spring 2013 Prof. Boutin

Back to ECE302

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva