Consider a random variable X whose distribution depends on a single parameter θ which instead of being regarded as a fixed constant, is also a random variable following a particular distribution. In this case, we say that random variable X has a compound or composed distribution.
let us consider the two dimensional random vector (X, λ) in which one variable is discrete and the other is continuous. For a constant h > 0 and λ1 > 0, the joint density density of X and λ is given by
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