Question: Please do all parts for the problem 3. (a) Suppose each of the 50 states of the USA votes either Democrat or Republican in the

Please do all parts for the problem the 50 states of the USA votes either Democrat or Republican in the next elec- tion. Assume that each state votes Democrat with a

3. (a) Suppose each of the 50 states of the USA votes either Democrat or Republican in the next elec- tion. Assume that each state votes Democrat with a 50% probability, and Republican with a 50% probability. If there are 109 borders between states, use linearity of expectation to find the expected number of borders that separate a Democratic voting state from a Republican voting state. For example, the following map shows 6 states with 7 borders between states. There are 5 borders that separate a Democratic voting state from a Republican voting state Solution: Let X be the random variable that represents the number of borders that separate a Democratic voting state from a Republican voting state. Suppose each border is numbered 1, 2, 109. For each i from 1 to 109, let Xi be the random variable defined to be

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