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Expected Value & Standard Deviation for a Walking Problem

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Please solve the attached questions to do with expected value and standard deviation in a walking scenario.

Solution Summary

For two given random walk problems, expectation value and standard deviation are estimated.

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019.
xi = +1: p = 1/2
xi = -1: p = 1/4
xi = 0: p = 1/4

z = sum (i= 1 to N) {xi}

(a)
Because, expected value of X, E(X) = sum (i = 1 to n) {pi * Xi}

Expectation of xi:
E(xi) = (1/2)*(+1) + (1/4)*(-1) + (1/4)*0 = 0.25

Hence,
E(z) = sum (i = 1 to N) {E(xi)} = 0.25*n = n/4 ...

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• MSc , Pune University, India
• PhD (IP), Pune University, India
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