This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let, Where is the loss incurred for choosing the (c+1) th action, rejection and is the loss incurred for making a substitution error. Show that the minimum risk is obtained if we decide • if for all and if and reject otherwise. What happens if = 0? What happens if ? 4- Let the components of the vector x = (x 1 ,…x d ) t be binary valued (0 or 1) and be the prior probability for the state of nature and j = 1,….c. Now define With the components of x i being statistically independent for all x in . Let x be distributed as described above, with c=2, d odd and (a) Show that the minimum-error-rate decision rule becomes: (b) Show that the minimum probability of error is given by (c) What is the limiting value of ? Explain. (d) Show that approaches zero as Explain....
View Full Document
- Spring '09
- likelihood ratio, minimum probability, probable one-dimensional densities