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Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? =...

Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? = ?, ? = ?) = 1 − ?, ?(? = 1|? = ?, ? = ?) = ?(1 − ?) and ?(? = 2|? = ?, ? = ?) = ??.

1. Find the conditional joint p.d.f. (the posterior) ??,?|?=?.

2.Write down the conditional expectation ?[?|? = ?] and ?[?|? = ?] as functions of ?.

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