Thread: Independent Random Variables

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

Originally Posted by farshyfaroo

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?

and are independednt if:



for all and in the appropriate sample spaces. Let , does this hold?

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

The possible values of Z_1 are 0, 1, 2 calculate their probabilities.

(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

Now the 's are iid so the is the mean of a sample of size for a sample from the same distribution as ... so is approximatly normally distributed with mean and variance ...

CB