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3 Conditional Expectations and the Law of Iterated Expectations Let :I: be a random variable which follows the standard normal distribution. Let y be hinolnially
3 Conditional Expectations and the Law of Iterated Expectations Let :I: be a random variable which follows the standard normal distribution. Let y be hinolnially distributed random variable: with a 50% chance of being I] and a 50% chance of being 1. Assume the y and :1: are independent. 1. What is M3: 3 {l} '3 2. What is My 2 \"la: 3 [I] '3 3. \"What is P(:.L' 2 My = U)? 4. Show that E[E[:r.:|y]] : E[;::] 5. Use your knowledge of calculus and integrals to show that the P(l g a: E l} = Phi: S l) P(r;: g l]
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