Q2. Suppose you have the same pdf given in Q1 with known B. The goal is to estimate the unknown 0. But suppose that, instead of observing X1,...,X, exactly, you only get to see whether or not each X; is less than 5. That is, you only observe Y1,..., Ym where 19• • (1, X, 5 5 Y, =. 0, X, > 5 ,i = 1,..., n. a) What is the distribution from which Y1,..., Y, is sampled? 19•••, n b) Using the corrupted data Y,...,Y, only, discuss how to find the numeric values of the MLE 0.

You wish to test the following claim (H.) at a significance level of a = 0.10. H.:p = 0.44 На :р< 0.44 You obtain a sample of size n = 488 in which there are 183 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value

Complete the tables for different values of and â = 1 - ô. From the tables, which value of appears to give the maximum value of the product pa. p. A pq р q=1-p 0.45 0.46 0.47 0.48 0.49 0.50 (Type integers or decimals.) Complete the table below. ^^ Р q=1-p pq 0.51 0.52 0.53 0.54 0.55 (Type integers or decimals.)