(a) Let X be a random variable with finite variance. Let Y = ax + 3 for some numbers a, ß E R. Compute 1₁ = E[(Y - E[Y|X])²]. (b) Again, let X be a random variable with finite variance. Additionally, let A ~ U(-1, 1) such that X and A are independent and consider Y = AX. You may use without proof that A² 1 X². Compute 12 = E[(Y - E[YIX])2] expressing your final result in terms of E[X] for some value or values of k that you should specify. (c) [TYPE:] Provide an interpretation of the quantities ₁ and 2 obtained in parts (a) and (b) above in terms of the ability to predict Y given the value of X and explain any difference you observe.

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A:

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A:

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A: The provided information is as follows:The probability mass function of  is .

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Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

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A: i) First part:ii) second part:

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A:

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