Suppose that i have twenty physically identical tickets inside a box, each with some number between 1 and 15 (inclusive) printed on it. before they were placed in the box, they were laid out on the table and found to bear the following numbers: 13 11 4 14 13 10 15 3 4 6 7 1361 5 3 2 11 5 13 (a) for each integer i from 1 to 15, list the probability p(i) of drawing a ticket with that number on it from the box at random. (it is possible that p() = 0 for some i.) give the probabilities as decimal numbers. (b) draw a histogram showing p(i) as a function of i. suppose that each time a ticket is drawn from the box, it is put back and the tickets (c) if i repeat this process a hundred times, how many draws should i expect to yield the number 3? (d) over many draws, what is the average value of the number drawn, (i)? what is (i2)? (e) what is the standard deviation of i?