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5980Random Walk With Rest PeriodsA process evolves in rounds. Each round, independently, with probability 1/2 the walker rests (position unchanged) and with probability 1/2 it takes a step that is +1 or -1 with equal odds. The walker stops at the first round in which it completes its 8th actual (non-rest) step. Let S be the position at that stopping time. Find E[S 2].概率中等数值题未尝试免费5988Expected Sample Size of a Sequential Drift TestA sequential test accumulates i.i.d. log-likelihood increments X 1,X 2,\dots with E[X i]=0.25. The test stops at N=\min\ n: |S n|\ge 3\ where S n=\sum i=1 n X i, and it is given that E[N]< and that the expected stopped statistic is E[S N]=2.0 (reflecting that the upper boundary is hit far more often under this positive drift). Each observation costs \6 to collect. Using a Wald-style identity, find the expected total data-collection cost.概率中等数值题未尝试免费