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題組內容

(25%) Consider two continuous random variables X and Y with joint pdf:

(b) (5%) Find the conditional pdf

其他申論題

(b) (7%) Find the best estinate (that is not necessarily linear) of Y given X such that the mean square estimation error is minimized. What is the minimum mean square error thus found?

a)Derive the conditional cumulative distribution function.(5%)

b) EE[XIY]]=?(5%)

(a) (5%) Find the constant c

(c) (5%) Find the conditional pdf

(d) (5%) Find the conditional mean E[Y|X = x], for x≥ 0

(e) (5%) Find the conditional variance Var(Y|X = x), for x ≥ 0

7.(8%) The random variable x is uniform in the interval [-5, 5]. Define y = Find C.D.F. Fy(y) and p.d.f. fy(y).

(10%) Suppose that X is a continuous random variable with cumulative distribution function (CDF) Fx(x) and probability density function (pdt) fx(x), respectively. Let Y = |2X|. Find the CDF of Y.

a. The set of all 2x2 triangular matrices.

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