A particular unfair coin is constructed so that the probability of obtaining a head is 1/3. The
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Question:
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.
(a) Construct a table showing the joint probability distribution of both random variables Z and W including the marginal probabilities.
(b) Find the covariance between Z and W. Are they independent?
(c) Suppose the covariance between Z and W was 0. Would this imply that Z and W are independent?
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