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Suppose $C_k$ is a random matrix contains columns of measurement vectors that are random variables: $$C_k=[c_k^1,...,c_k^{m_k^c}]$$ $m^c_k$ is the number of columns as well as a random variable. All the measurement vectors are independent.

How we can show that the distribution of $C_k$is identical to the joint distribution of $C_k$and $m^c_k$, i.e. $p(C_k)=p(C_k,m^c_k)$?

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