Use the fact that the mean of a geometric distribution is μ= 1 p and the variance is σ2= q p2. A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1 100. Let x be the number of times you play the lottery before winning the first time. (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 $600. Would you expect to make or lose money playing this lottery? Explain. (a) The mean is 100100. (Type an integer or a decimal.) The variance is 99009900. (Type an integer or a decimal.) The standard deviation is 99.599.5. (Round to one decimal place as needed.) (b) You can expect to play the game 100100 times before winning. Would you expect to make or lose money playing this lottery? Explain. A. You would expect to make money. On average you would win $600 once in every nothing times you play. So the net gain would be $nothing. B. You would expect to lose money. On average you would win $600 once in every 100100 times you play. So the net gain would be $nothing