Use the fact that the mean of a geometric distribution is muequalsstartfraction 1 over p endfraction and the variance is sigma squared equals startfraction q over p squared endfraction . a daily number lottery chooses three balls numbered 0 to 9. the probability of winning the lottery is startfraction 1 over 1000 endfraction . 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 ​$700. would you expect to make or lose money playing this​ lottery? explain.