Find the second moment and the variance of si condition

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Reference no: EM13909684

(a) Use (2.42) to find E [Si | N(t)=n]. Hint: When you integrate sifSi (si | N(t)=n), compare this integral with fSi+1 (si | N(t)=n + 1) and use the fact that the latter expression is a probability density.

(b) Find the second moment and the variance of Si conditional on N(t)=n. Hint: Extend the previous hint.

(c) Assume that n is odd, and consider i = (n+1)/2. What is the relationship between Si, conditional on N(t)=n, and the sample median of n IID uniform rv s.

(d) Give a weak law of large numbers (WLLN) for the above median.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909684

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