| Line 24: | Line 24: | ||
---- | ---- | ||
=Problem 2 = | =Problem 2 = | ||
| − | + | Problem statement: Let <math class="inline">X</math> be a continuous or discrete random variable with mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^2</math>. Then, <math class="inline">\forall \varepsilon >0</math>, we have<br> | |
| + | <math> P(|X-\mu| \geq \varepsilon) \leq \frac{\sigma^2}{\varepsilon^2}</math><br> | ||
===== <math>\color{blue}\text{Solution 1:}</math> ===== | ===== <math>\color{blue}\text{Solution 1:}</math> ===== | ||
===== <math>\color{blue}\text{Solution 2:}</math> ===== | ===== <math>\color{blue}\text{Solution 2:}</math> ===== | ||
| + | Discrete Case:<br> | ||
| + | Continuous Case:<br> | ||
Revision as of 19:57, 25 January 2014
Communication, Networking, Signal and Image Processing (CS)
Question 1: Probability and Random Processes
August 2012
Problem 2
Problem statement: Let $ X $ be a continuous or discrete random variable with mean $ \mu $ and variance $ \sigma^2 $. Then, $ \forall \varepsilon >0 $, we have
$ P(|X-\mu| \geq \varepsilon) \leq \frac{\sigma^2}{\varepsilon^2} $
$ \color{blue}\text{Solution 1:} $
$ \color{blue}\text{Solution 2:} $
Discrete Case:
Continuous Case:
