# Use the fact that the mean of a geometric distribution is μ=1/p and the variance is σ2 =q/p2 A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1/100. 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.

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Use the fact that the mean of a geometric distribution is μ=1/p and the variance is σ=q/p

A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1/100. 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.

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Step 1

It is given that x is the number of times to play the lottery before winning first time.

p = 1/100 and q = 99/100.

a).

The mean is calculated as follows.

Step 2

The variance and standard deviation calculated as follows.

Step 3

b). from part (a), the expected number of lotteries to play to get first win is 100.

Therefore, the expected ... help_outlineImage TranscriptioncloseExpected value of the game expected win - expected lose - 300 -1 100 =2 fullscreen

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