Question

Use the fact that the mean of a geometric distribution and the variance i A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery is . 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 $300. Would you expect to make or lose money playing this lottery? Explain. (a) The mean is (Type an integer or a decimal.) The variance is (Type an integer or a decimal.) The standard deviation is . (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. times you O A. You would expect to lose money. On average you would win $300 once in every play. So the net gain would be $ times OB. You would expect to make money. On average you would win $300 once in every you play. So the net gain would be $

Answer 1

sto Gaman dah, p[winning the lodley) - ibbo . x: be a rondom vanable denok the nous times you play before cunning the 1st time xw Geometarac (p: to) pope > p (x=x] = qlp ; x =!0,-- it is given the rear of geometric distribution E(x) = 1 . and variance ataq afid * mean e(x) = troca Vobo 1000 * verance pour le ) 107, 100 1006 = 1000-)). 1000 x 1000 1000 999 x 1000 999,000 to standard deviation si V variance 999 000 S: 999.5

b) you can expect to play the game f(x) = 1000 times - beque winning → you would expect to lose money on auerage you would with $300 once in every 1000 time you play, so the negle gain would be 300-1000 = $ 100 option ais Correct