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無年度 - 主題課程_理工學院機率論：多元隨機變數#107950
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題組內容
X and Y are two random variables with a joint probability density function as
b) EE[XIY]]=?(5%)
其他申論題
(a) (7%) Find the best linear estimate (i.e. aX +b with a, b being constants to be de termined) of Y given X such that the mean square estimation error is minimized. What is the minimum mean square error thus found?
#462922
(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?
#462923
a)Derive the conditional cumulative distribution function.(5%)
#462924
(a) (5%) Find the constant c
#462926
(b) (5%) Find the conditional pdf
#462927
(c) (5%) Find the conditional pdf
#462928
(d) (5%) Find the conditional mean E[Y|X = x], for x≥ 0
#462929
(e) (5%) Find the conditional variance Var(Y|X = x), for x ≥ 0
#462930
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).
#462931
(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.
#462932
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