articular unfair coin is constructed so that the probability of obtaining a head is 1/3. The ir coin is flipped twice. Define two random variables: Z = the number of heads in the flip and W = the number of heads in two flips. i. Construct a table showing the joint probability distribution of both random variables Z and W including the marginal probabilities. ii. Find the covariance between Z and W. Are they independent? iii. Suppose the covariance between Z and W were 0. Would this imply that Z and W

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Problem 2
A particular unfair coin is constructed so that the probability of obtaining a head is 1/3. The
unfair coin is flipped twice. Define two random variables: Z = the number of heads in the
first flip and W = the number of heads in two flips.
i. Construct a table showing the joint probability distribution of both random
variables Z and W including the marginal probabilities.
ii. Find the covariance between Z and W. Are they independent?
iii. Suppose the covariance between Z and W were 0. Would this imply that Z and W
are independent?
Transcribed Image Text:Problem 2 A particular unfair coin is constructed so that the probability of obtaining a head is 1/3. The unfair coin is flipped twice. Define two random variables: Z = the number of heads in the first flip and W = the number of heads in two flips. i. Construct a table showing the joint probability distribution of both random variables Z and W including the marginal probabilities. ii. Find the covariance between Z and W. Are they independent? iii. Suppose the covariance between Z and W were 0. Would this imply that Z and W are independent?
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