Question

3) Each of the following describes a different data sample, Y₁, Y₂, ..., Y_n. 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.

Answer 1

a.) Flipping of a coin and taking 1 if it comes head and taking 0 if it comes tails is independently and identically distributed because in this case the two events are independent of each other because the occurrence of head or tail does not depend on the previous event.

b.) This event is not an iid event because the unemployment rate in the (n)th month depends on the unemployment rate in (n-1) th month.

c.) This event is also not an iid event because the rainfall in (n) th month depends on the rainfall in (n-1) th month.