3. Suppose we roll a dice n times. Define the random variable Xi to be equal to 1 if the

ith roll results in an even number, and 0 otherwise. Define the the random variable Yi to be

equal to 1 if the ith roll results in the number 6, and zero otherwise.

(a) Are X1 and Y1 independent random variables?

(b) Find the distribution of Z1 = X1 + Y1.

(c) Suppose n is 500. What is the approximate distribution of

1/500 (500)sigma(i=1)Xi +1/500 (500)sigma(i=1)Yi