Question: 6. Bit by Bit [12 points] Suppose a bit string of length three is generated such that each bit is equally likely to be

6. Bit by Bit [12 points] Suppose a bit string of length three is generated such that each bit is equally likely to be 0. or 1, and the bits are independent. Let E be the event that the string contains an odd number of 1s, and let F be the event that the string starts with 1. Prove or disprove that E and F are independent.

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