100BHW - times. Let p be the probability that we observe...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 100B HWI Due Friday 5pm Problem 1 Let X 1 ,...,X n Bernoulli( p ) independently. Let S = n i =1 X i . Suppose we have two estimators of p . (1) ˆ p = S/n , and (2) ˆ p = ( S + n/ 2) / ( n + n ). (1) Calculate the bias and variance of each estimator. (2) Calculate the mean squared error of each estimator. Plot the mean squared errors of the two estimators together over the true value of p [0 , 1], for n = 5, n = 10, and n = 100 respectively. Problem 2 Suppose we roll a die 1000 times independently, and we observe the number six 180
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: times. Let p be the probability that we observe the number six each time. (1) Find the 95% condence interval of p . What is the margin of error? Find the 90% condence interval of p . (2) Test the hypothesis H : p = 1 / 6 versus the hypothesis H 1 : p > 1 / 6. Calculate the p-value. Is there evidence that the die is not fair? 1...
View Full Document

This note was uploaded on 03/30/2011 for the course STAT 100B taught by Professor Wu during the Winter '11 term at UCLA.

Ask a homework question - tutors are online