1. A coin is tossed 100 times. a) the difference “number of heads – number of tails” is like the sum of 100 draws from one of the following boxes. which one, and why?(i) heads, tails (ii) -1, 1 (iii) -1, 0 (iv) 0, 1 (v) -1, 0, 1b) find the expected value and standard error for the difference.2) a coin will be tossed 100 times. you get to pick 11 numbers. if the number of heads turns out to equal one of your 11 numbers, you win a dollar. which 11 numbers should you pick, and what is your chance of winning? explain.3) a box contains ten ticket, four marked with a positive number and six with a negative number. all the numbers are between -10 and 10. one thousand draws will be made at random with replacement from the box. you are asked to estimate the chance that the sum will be positive. a) can you do it on the basis of the information already given?b) can you do it if you are also told the average and SD of the numbers in the box, but are not told the numbers themselves?
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