Use the fact that the mean of a geometric distribution is $=\frac{1}{p}$

and the variance is ${}^2=\frac{q}{p^2}$

$.$

A daily number lottery chooses balls numbered $0$ to $9.$ The probability of winning the lottery is $\frac{1}{1000}$

$.$ 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.