Modelling a Binary Data Set 1 point possible (graded) You would like to determine the percentage of coffee drinkers in your university, and collected the following binary data set from random students on campus, 1 for coffee drinker and 0 for otherwise: 0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1. Let Y; denote the i'th number in this list. You decide to model this data set under the following assumptions: - Y1, . . . , Y,1 are identically distributed as some random variable Y. I Y1, . . . , K, are independent. - Y; only takes the value 0 or 1. Under these assumptions, how many unknowns are needed to specify the distribution of Y? Approximating the unknown parameter 1 point possible (graded) As above, let Y1,. . . , Y" denote the i'th number in the binary data set. Recall that Y1, . . . in are assumed to be independent and identically distributed (i.i.d.) as some distribution Y. In the future, we WIII abbreVIate this assumption With the notation Y1, . . . ,Y\"n 11 Y. Which of the following converges to Ell/1] = IE [Y] as n > 00? {Choose all that apply.) I:| total number of 1's n DY\" |:| Median(1'1,...,Y1) D1\" Cherry Blossom Run 1 point possibie (graded) The average running time for the 2017 Cherry Blossom Run in Washington DC was 98 minutes; the standard deviation was 17 minutes. Let X denote the running time, in minutes, of a random finisher. What is the best model for the distribution of X ? O Ber (P)