Question

3. A coin is tossed repeatedly. Let the random variable x be the number of the toss at which a head first appears. Find the probability P that x-n, for n 1,20. Show that the probabilities sum to unity. Calculate the expectation value (average) of x. Calculate the variance of x. First do these calculations numerically out to x- 20 using a spread sheet (by that point you should be very close to the exact result). Attach a print-out of the spreadsheet to your homework solutions. Then do the calculations analytically, making use of the geometric series. Hint: note that

Answer 1