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3) Each of the following describes a different data sample, Y1, Y2, ..., Yn. For each...

3) Each of the following describes a different data sample, Y1, Y2, ..., Yn. For each sample, explain whether the sample is i.i.d. — independently and identically distributed.

a) I flip a coin n times. For each flip, if it comes up Heads, Y takes on a value of 1; if Tails, Y takes on a value of 0.

b) I collect the Pennsylvania unemployment rate for n consecutive months.

c) For n months, I collect the total rainfall in Pittsburgh.

Math   Statistics-And-Probability   
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Answer #1

(a) Here, each sample is i.i.d, because the outcome of the flip of the coin for the second time is not afftected by the the outcome of the flip of the coin for the second time. Also the probability of coming up Heads in each of the n trials is the same.

(b) Here, each sample is not i.i.d. because the unemployment rate for the second month depends on the unemployment rate for the first month. Also the probability of unemployment is not the same for each of the n months.

(c) Here, each sample is not i.i.d., because the rainfall for the second month depends on the rainfall for the first month. Also, the probability of rainfall for each of the n months is not the same.

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