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| − | [[ | + | = [[:Category:Problem solving|Practice Problem]]: compute the zero-th order moment of a Gaussian random variable = |
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| − | A random variable X has the following probability density function: | + | |
| + | A random variable X has the following probability density function: | ||
<math> | <math> | ||
f_X (x) = \frac{1}{\sqrt{2\pi} 3 } e^{\frac{-(x-3)^2}{18}} . | f_X (x) = \frac{1}{\sqrt{2\pi} 3 } e^{\frac{-(x-3)^2}{18}} . | ||
| − | </math> | + | </math> |
| − | Compute the moment of order one of that random variable. In other words, compute | + | Compute the moment of order one of that random variable. In other words, compute |
| − | <math>E \left( X^1 \right) .</math> | + | <math>E \left( X^1 \right) .</math> |
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| − | ==Share your answers below== | + | |
| − | 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! | + | == Share your answers below == |
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| + | 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! | ||
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| − | ===Answer 1=== | + | |
| − | + | === Answer 1 === | |
| − | ===Answer 2=== | + | |
| − | Write it here. | + | The moment of n-th order moment is defined as: <math>E[X^{n}]=\int_{-\infty }^{\infty }x^{n}f_{X}(x)dx</math> |
| − | ===Answer 3=== | + | |
| − | Write it here. | + | Therefore, |
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| + | <math>E[X^{1}]=\int_{-\infty }^{\infty }xf_{X}(x)dx=\frac{1}{3\sqrt{2\Pi }}\int_{-\infty }^{\infty }xe^{-\frac{(x-3)^{2}}{18}}dx=\frac{1}{3\sqrt{2\Pi }}9\sqrt{2\Pi }=3</math> | ||
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| + | === Answer 2 === | ||
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| + | Write it here. | ||
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| + | === Answer 3 === | ||
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| + | Write it here. | ||
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| − | [[ECE302|Back to ECE302]] | + | [[2013 Spring ECE 302 Boutin|Back to ECE302 Spring 2013 Prof. Boutin]] |
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| + | [[Category:ECE302]] [[Category:ECE302Spring2013Boutin]] [[Category:Problem_solving]] [[Category:Continuous_random_variable]] | ||
Revision as of 13:48, 23 March 2013
Contents
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 one of that random variable. In other words, compute
$ E \left( X^1 \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 n-th order moment is defined as: $ E[X^{n}]=\int_{-\infty }^{\infty }x^{n}f_{X}(x)dx $
Therefore,
$ E[X^{1}]=\int_{-\infty }^{\infty }xf_{X}(x)dx=\frac{1}{3\sqrt{2\Pi }}\int_{-\infty }^{\infty }xe^{-\frac{(x-3)^{2}}{18}}dx=\frac{1}{3\sqrt{2\Pi }}9\sqrt{2\Pi }=3 $
Answer 2
Write it here.
Answer 3
Write it here.
