2 answers
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a) The random variables X_i, i=1,2,...,n, are not independent. This is because they all have a common component, the variable Θ. Any change or variation in Θ would affect all the X_i variables, which means there is a dependence among them.
b) The random variables X_i, i=1,2,...,n, are conditionally independent given Θ. This means that once the value of Θ is known, the X_i variables become independent of each other. However, without knowing the value of Θ, the X_i variables are not independent.