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Let $X_1, X_2,.... X_{n+1}$ be a sequence of independent identically distributed random variables taking the value $1$ with probability $p$ and $0$ with probability $1-p$. Let $Y_k = 0$ if $X_k + X_{k+1}$ is even and $Y_{k} = 1$ if $X_k + X_{k+1}$ is odd. The aim is to find the expectation and variance of $Y_1 +....+ Y_n$. This is one of the statistics qualifying exam problem from previous years and I am just curious as to how to begin solving it. Any help, however small, is much appreciated

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