Compute the variance and covariance

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Let {Xn}nN0 be a symmetric simple random walk. For n ∈ N the average of the random walk on the interval [0,n] is defined by

Is {An}nN0 a simple random walk (not necessarily symmetric)? Explain carefully using the definition.

Compute the covariance Cov(Xk,Xl) = E[(X- E[Xk])(X- E[Xl])], for k ≤ l ∈ N

Compute the variance of An, for n ∈ N.

Reference no: EM131127656

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