s] Suppose X and Y are two jointly distributed random variables (in Part A, feel free to assume these are continuous random variables). Prove/show that oxy = cov(x, y) = E[XY] — E[X]E[Y]. Show all essential steps/arguments. ¹Suppose X and Y are two jointly distributed random variables (in Part A, feel free to assume these are continuous random variables). Prove/show that E[Y] = Ex [Ey|x[Y|X]] (“Law of Iterated Expectations"). Show all essential steps/arguments. ¡ Suppose X and Y are two jointly distributed random variables (in Part A, feel free to assume these are continuous random variables). Prove/show that E[XY] = Ex[XE[Y|X]]. Show all essential steps/arguments.

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A: X,Y ~ Uniform(0,2) E(X) = E(Y) = 0+22=1 Var(X) = Var(Y) = (2-0)212=412=13 Z = Yif X <122Yif X≥12…

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A:

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A:

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A: Let X is a random variable.

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A:

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Q: Is cov(X, Y) random?

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A: Solution: From the given information,

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A:

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A: Step 1: Step 2: Step 3: Step 4:

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A:

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A: Given that X and Y are independent random variables.