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typical random walk :

one step forward or backward with equal probability and independence of each step , what is the expectation and Variance .

so i define indicator variable x

E(x

Var(x

now define S

each step is independent and identical to the other so

i can say that S

now from definition of Expectation and Variance :

E(S

Var(S

but i know for certain that actually the answer is σ

how is that ?

please

thank you!

one step forward or backward with equal probability and independence of each step , what is the expectation and Variance .

so i define indicator variable x

_{i}={1 or -1 with equal probabilty .E(x

_{i}) = 0Var(x

_{i}) = 1now define S

_{n}as the sum of i=1,...,neach step is independent and identical to the other so

i can say that S

_{n}= nx_{i}now from definition of Expectation and Variance :

E(S

_{n}) = E(nx_{i}) = nE(x_{i}) = 0Var(S

_{n}) = Var(nx_{i}) = n^{2}Var(x_{i}) = n^{2}⇒σ_{sn}=nbut i know for certain that actually the answer is σ

_{sn}=sqrt(n)how is that ?

please

thank you!