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1. Let ?1 and ?2 be two independent random variables with normal distribution with expectation 0...

1. Let ?1 and ?2 be two independent random variables with normal distribution with expectation 0 and variance 1.

(1) Find the covariance between ?1 + ?2 and ?1 − ?2.

(2) Find the probability that ?2 1 + ?2 2 ≤ 2. (3) Find the expectation of ?2 1 + ?2^2 .

2. Estimate the approximated value of (︂ 10000 5100 )︂ = 10000! 5100!4900! by central limit theorem.

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