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Suppose, Χ | θ ~ Binom(m,0)and 0 ~ Beta(α,β), then var y) is equals to,

We are given a scenario involving a Binomial and Beta distribution. Specifically:

1. \( X | \theta \sim \text{Binomial}(m, \theta) \), meaning that given \(\theta\), \(X\) follows a binomial distribution with parameters \(m\) (

Explore how variance is calculated in the context of Binomial and Beta distributions. This problem involves applying the variance formula for Binomial distribution and understanding the properties of the Beta distribution. Suitable for advanced undergraduate students and researchers.

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