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 two balls numbered 0 to 9. the probability of winning the lottery is startfraction 1 over 100 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 $400. would you expect to make or lose money playing this lottery? explain.