This preview shows page 1. Sign up to view the full content.
Unformatted text preview: probability that the roots of the quadratic A * x 2 + B * x + C are real? (Source: Rice Mathematical Statistics and Data Analysis third edition exercise 3.11). (a) In R, simulate the above situation. If you dont know when the root of an equation will be real, look up how to solve for the roots of a quadratic function. According to your simulation, how often are the roots real? [As always, if you want help with R, tell me exactly what you want to do, and Ill tell you how to do it in R.] (b) Analytically: nd the probability that three random coecients will produce an equation with real roots. [Hint: Let Y = B 2 , W = 4 AC . Find the distributions of each of Y and W . Note that Y and W are independent. Because we havent yet covered section 3.9, I will tell you the distribution of W.] The distribution of W is given by: f ( w ) = (log ( w/ 4) / 4 if 0 w 1 otherwise...
View
Full
Document
 Spring '10
 JO.H
 Math, Probability

Click to edit the document details