is easy to show that it has the following properties:? ? & are independentРRandom VariableРWith the random variable, define a random variable and a random sequenceРRandom WalkРConsider a time period [0,T], which can be divided into N equal intervals. Let Δ=T\ N, t_n=nΔ,(n=0,1,\cdots,N), then ? ?A random walk is defined in [0,T]:Р is called the path of the random walk.РDistribution of the PathРLet T=1,N=4,Δ=1/4,РForm of PathРthe path formed by linear interpolation between the above random points. For? Δ=1/4 case, there are 2^4=16 paths.РtРSР1РProperties of the PathРCentral Limit TheoremРFor any random sequence Р where the random variable X~ N(0,1), i.e. the random variable X obeys the standard normal distribution:? E(X)=0,Var(X)=1.РApplication of Central Limit Them.РConsider limit as Δ→ 0.
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