1 Use the fact that the mean of a geometric distribution is u=- and the variance is o = 9 P 2' P 1 A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is winning the first time. . Let x be the number of times you play the lottery before 100 (a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs $1 to play and winners are paid $1000. Would you expect to make or lose money playing this lottery? Explain. (a) The mean is The variance is The standard deviation is (Type an integer or a decimal.) (Type an integer or a decimal.) (Round to one decimal place as needed.) (b) You can expect to play the game times before winning. Would you expect to make or lose money playing this lottery? Explain. OA. You would expect to make money. On average you would win $1000 once in every $ OB. You would expect to lose money. On average you would win $1000 once in every $ times you play. So the net gain would be times you play. So the net gain would be