You throw darts at a board with 20 equally likely spaces. You throw until you hi

Question

You throw darts at a board with 20 equally likely spaces. You throw until you hit “1”, then you throw until you hit “2”, then you throw until you hit “3”, etc., and finally you throw until you hit “20”. Let X be the number of throws you make to achieve this goal.

a) What are the expected value and standard deviation of X? Hint: What is the distribution?

b) Let Y be the number of throws needed until the 20th time hitting '1'. What are the expected value and standard deviation of Y? Hint: What is the distribution?

c) Why were your answers to X and Y the same? Is this a coincidence?

Explanation / Answer

a)as probabilty of one space out of 20 =1/20

this is geometric distribution cause we are hitting till end results achieved

expected value =r/p=20/(1/20)=400

std deviation =(r(1-p)/p2)1/2 = 87.18

b)as this is also geomeric distribution

expected value =r/p=20/(1/20)=400

std deviation =(r(1-p)/p2)1/2 = 87.18

c)No, this is not coincidence ; cause both have same distribution with same parameter with r=20 and p=1/20

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