tag:blogger.com,1999:blog-35287389.post-1164573945452155272006-11-26T12:45:00.000-08:002006-11-26T15:16:17.633-08:00Section 12.6.1 Part 1 Blog Entry:<br /><br />Having read section 12.6.1 part 1 in the text:<br /><br /><strong>Difficult:</strong><br />On page 888, I was actually a bit unsure in the beginning parts of the proof of Chebyshev's Inequality. I was a bit confused on how we know that the E(X - mean)^2 =sigma^2 is less than infinity. I was a bit caught off guard with the text's mention of expectations in this section since I was actually trying to figure out and make sense first of the probability notations that it had given us just above it. Because I am not quite sure how this expectation of (X-mean)^2 came about, I was not able to fully grasp the idea/equation directly below in the proof on page 888 that states that P((X-mean)^2 greater than or equal to c^2) is less than or equal to E(X-mean)^2/c^2 = (sigma^2)/(c^2). <br /><br /><strong>Reflective:</strong><br />I wasn't quite sure th purpose of the text's explanation of the change in notation of Markov's Inequality. Given the Inequality, we could see that by multiplying both sides by the denominator (of the right side of the inequality), a, you could get the conclusion on page 888 that states that the EX is greater than or equal to "a" multiplied by the probability of random variable X greater than or equal to "a". It seemed somewhat unnecessary to include the mathematical explanation of this change in notation.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/35287389-116457394545215527?l=jhanmath3c.blogspot.com'/></div>Jhanhttp://www.blogger.com/profile/06752938263515594367noreply@blogger.com0