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A Gamma distribution can be defined as [tex] \Gamma(\alpha,\beta) [/tex], where [tex]\alpha[/tex] and [tex]\beta[/tex] are the 'scale' and 'shape' parameters.

Now suppose if [tex]\alpha[/tex] was a random variable, say following a binomial distribution, how would I then represent the distribution of X.

I was thinking that since the parameter [tex]\alpha[/tex] now represents a random variable, the distribution of X, would simply be a binomial distribution multiplied by a Gamma distribution?

Would it be correct to do this??