i.i.d. distribution

[Maulik]

I'm currently taking an economics class and we constantly discuss independent, identical distribution. I am interested in an example which leaves me understanding this concept, I don't like our book's explanation.

[mosdef]

repeated trials with the same individual probability distribution and where the outcome of one does not impact the outcome of another.

if you roll a die n times in a row, the RVs X_1, X_2, X_3, etc (where X_i is the value of the ith die roll) are i.i.d.

Consider the set of RVs, Y_1 = X_1+X_2, Y_2 = X_2+X_3, Y_3 = X_3 + X_4, etc. These Y_i's have the same probability distribution (they are "i.d") but are not independent and so not i.i.d.

Consider the RVs Z_1 = X_1, Z_2=X_2+x_3, Z_3=X_4+x_5+X_6, etc. these are independent but they have different probability distributions. to they are "i" but not "i.i.d"