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The probability with which a coin shows heads upon tossing is p. The random variable X1...

The probability with which a coin shows heads upon tossing is p. The random variable X1 takes the values 1 and 0 if the outcome of the "first toss is heads or tails respectively; another random variable X2 is defined in the same way based on the second toss.

(a) Is X1-X2 a sufficient statistic for p? Show the work.

(b) Is X1+X2 a sufficient estimator for p? Show the work.

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