Random Walk: Quantiles, average and maximal walk

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As a statistics newbie I'm interested in the random walk, especially in a random walk with an underlying normal distribution where the variance of the process is known. For these special cases I tried to find out how I could calculate the expected distance travelled, the expected distance of the maximal walk as well as quantiles of the resulting normal distribution for given walking times n. Would be very happy if you'd help! Thanks a lot in advance!