{"id":47401,"date":"2022-03-31T16:47:59","date_gmt":"2022-03-31T16:47:59","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/using-a-long-rod-that-has-length-you-are-going-to-lay-out-a-square\/"},"modified":"2022-03-31T16:47:59","modified_gmt":"2022-03-31T16:47:59","slug":"using-a-long-rod-that-has-length-you-are-going-to-lay-out-a-square","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/using-a-long-rod-that-has-length-you-are-going-to-lay-out-a-square\/","title":{"rendered":"Using a long rod that has length , you are going to lay out a square"},"content":{"rendered":"<div>\n<p>Using a long rod that has length , you are going to lay out<\/p>\n<p>a square plot in which the length of each side is . Thus the<\/p>\n<p>area of the plot will be 2. However, you do not know the<\/p>\n<p>value of , so you decide to make n independent measurements<\/p>\n<p>X1, X2, . . . , Xn of the length. Assume that each Xi has<\/p>\n<p>mean (unbiased measurements) and variance s2.<\/p>\n<p>a. Show that is not an unbiased estimator for m2. [Hint: For<\/p>\n<p>any rv Y, E(Y2)  V(Y)  [E(Y)]2. Apply this with Y  .]<\/p>\n<p>b. For what value of k is the estimator  kS2 unbiased<\/p>\n<p>for 2? [Hint: Compute E(  kS2).]<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Using a long rod that has length , you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be 2. However, you do not know the value of , so you decide to make n independent measurements X1, X2, . [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-47401","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/47401","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=47401"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/47401\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=47401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=47401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=47401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}