Question

Consider a statistical experiment of flipping a fair coin and tossing a fair dice simultaneously. Let X be the number heads in flipping the coin, Y be the number shown in tossing the dice, and Z = XY. What is the correlation coefficient of X and Y?

Answer 1

X: The number of heads in flipping the coin

Y: The number shown in tossing the dice

Now consider the experiment of flipping a fair coin and tossing a fair dice simultaneously . Now these two events are independent.

So, By definition, when X and Y are independent,

E(Z) =E(XY) = E(X) E(Y)

cov(X,Y) =E(XY) - E(X)E(Y) = E(X)E(Y) -E(X)E(Y) = 0

Thus, by definition, correlation coefficient formula :

So, correlation coefficient =0