Let (left{Y_{0}, Y_{1}, ldots ight}) be a sequence of independent, identically distributed binary random variables with (Pleft(Y_{i}=0

Let \(\left\{Y_{0}, Y_{1}, \ldots\right\}\) be a sequence of independent, identically distributed binary random variables with \(P\left(Y_{i}=0\right)=P\left(Y_{i}=1\right)=1 / 2 ; i=0,1, \ldots\). Define a sequence of random variables \(\left\{X_{1}, X_{2}, \ldots\right\}\) by \(X_{n}=\frac{1}{2}\left(Y_{n}-Y_{n-1}\right) ; \quad n=1,2, \ldots\)

Check whether the random sequence \(\left\{X_{1}, X_{2}, \ldots\right\}\) has the Markov property.