[問題] PDF 問題

[maxmie (王小Ming)]

不好意思 打擾各位先進了

小弟最近在學統計

在P.D.F的例題上碰到了一些問題  腦筋有點轉不過來..

概念也需要高手指導..

所以有三道題目想請問大家該如何解

1. Consider the continuous probability density function given
 by Px(x)=0.25 for 0<x<a
 (a)what is a?
 (b)what is prod(x>a/2)
 (c)what is prob (X>a/2|X>a/4)
 (d)what is prob(X>a/2|X<a/4)





2.Assume that the probability density function of daily rainfall is
given by

prob(X=0) = 0.25    X=0
Px(x)=0.25x         0<X<1.732
Px(x)=0.866-0.25x   1.732<X<3.464
(a)Is this a proper probability density function?
(b)what is prob(X>0.5)?
(c)What is prob(X>0.5|X≠0)?




3.Consider the probability density function given by

Px(x)=(λ1)/2       0<X<2
Px(x)=(1-λ1)/4     2<X<6

(a)Sketch px(x) for λ1 = 0.5
(b)Sketch px(x) for λ1 = 0.1
(c)Sketch px(x) for λ1 = 0.333
(d)In a random sample from px(x),60% of the values were between 0 and 2.
What would be an estimate for the value of λ1?


以上三題  麻煩求解..

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推 ases60909: pdf 的基本性質
→ ases60909: 1.f(x)>=0
→ ases60909: 2.積分(-inf 到 inf)f(x) dx=1