18) Remember that we are simulating draws from a box containing two tickets-one

Question

18) Remember that we are simulating draws from a box containing two tickets-one reading "O" and the other reading "1". Each data point above is like the sum of 9 draws from such a box. Using the ideas from chapters 16-18, calculate the expected value of the sum of 9 draws from the box, and use the square root law to calculate the standard error associated with that expected value. Put these into your lab report by filling in the blanks in the following sentence. "The sum of 9 draws from the box I [01 [1]I will be about 8 --, give or take or so".

Explanation / Answer

For each of the draw here, we have:

P( Xi = 0) = P(Xi = 1) = 0.5

Therefore E(Xi ) = 0.5*0 + 0.5*1 = 0.5

E(X2) = 0.5*02 + 0.5*12 = 0.5

Therefore, Var(Xi ) = E(Xi2) - [ E(Xi) ]2 = 0.5 - 0.52 = 0.25

Therefore for 9 drawn the total expected sum and variance would be given here as:

E(S) = 9E(Xi ) = 9*0.5 = 4.5

Var(S) = 9*Var(Xi ) = 9*0.25 = 2.25

Therefore SD(S) = square root of 2.25 which is 1.5

Therefore the sum of 9 draws from the box will be about 4.5 give or take 1.5 or so

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