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Use the fact that the mean of a geometric distribution is-land the variance is ơ.q A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery isLet 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 S600. Would you 1000 expect to make or lose money playing this lottery? Explain (a) The mean isType 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 A. You would expect to lose money. On average you would win $600 once in every times you play. So the net gain would be $ O B. You would expect to make money. On average you would win $600 once in every times you play. So the net gain would be STwo random variables x and y are independent if the value of x does not affect the value of y. If the variables are not independent, they are dependent. A new random variable can be formed by finding the sum or difference of random vanables. If a random variable x has mean μΧ and a random variable y has mean μy then the means of the sum and difference of the variables are given by the following equations The distribution of a tests scores for college-bound male seniors has a mean of 1527 and a standard deviation of 313. The distribution of a tests scores for college-bound female seniors has a mean of 1500 and a standard deviation of 309. One male and one female are randomly selected. Assume their scores are independent. What i What is the average sum of their scores? s the average sum of their scores? What is the average difference of their scores? (Type an integer or a decimal.) What is the average difference of their scores? (Type an integer or a decimal.)

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