2 question

Question 1: (15) One research article reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy. Answer the following questions: 50 _ 47 _ 44 39 36 31 23 20 14 11 79 78 76 74 71 68 67 65 61 59 i 104 j 101 i 99 j 96 i 93 i 91 i 89 i 85 i 84 ' 81 i _ 158 _ 148 141 _ 139 _ 136 _ 123 _ 118 _ 112 _ 105 _ 105 _ ' 513 _ 388 f 322 _ 289 _ 263 _ 248 206 184 168 161 a. Why can a frequency distribution not be based on the class intervals 050, 50100, 100150, and so on? b. Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100, ..., and then comment on interesting characteristics. c. What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200? Question 3: (15) The pmf of the amount of memory X (GB) in a purchased flash drive as X 2 4 8 16 p(x) .05 .10 .35 40 .10 Compute the following: a. E(X) b. V(X) directly from the definition c. The standard deviation of X, d. V(X) using the shortcut formula