s*****n
发帖数: 29 | 1 【 以下文字转载自 EE 讨论区 】
发信人: skymoon (海上生明月，天涯共此时), 信区: EE
标 题: 请教一道看似简单的概率题
发信站: BBS 未名空间站 (Thu Oct 27 20:25:32 2005), 站内
发信人: skymoon (海上生明月，天涯共此时), 信区: Mathematics
标 题: 请教一道看似简单的概率题
发信站: BBS 未名空间站 (Thu Oct 27 20:25:26 2005), 转信
A,B均为[0,1]上均匀分布的随机变量.X = [B, B+0.1]. 问A落在X的概率是多少?
很久没碰概率了,可能有些概念有些糊涂,想了好久也没做出来.非常惭愧.请高手指教 | s****m
发帖数: 8 | 2 0.095?
【在 s*****n 的大作中提到】
: 【 以下文字转载自 EE 讨论区 】
: 发信人: skymoon (海上生明月，天涯共此时), 信区: EE
: 标 题: 请教一道看似简单的概率题
: 发信站: BBS 未名空间站 (Thu Oct 27 20:25:32 2005), 站内
: 发信人: skymoon (海上生明月，天涯共此时), 信区: Mathematics
: 标 题: 请教一道看似简单的概率题
: 发信站: BBS 未名空间站 (Thu Oct 27 20:25:26 2005), 转信
: A,B均为[0,1]上均匀分布的随机变量.X = [B, B+0.1]. 问A落在X的概率是多少?
: 很久没碰概率了,可能有些概念有些糊涂,想了好久也没做出来.非常惭愧.请高手指教
| s*****n
发帖数: 29 | 3 How to get this number, and why?
【在 s****m 的大作中提到】
: 0.095?
| s****m
发帖数: 8 | 4 0.1*0.9 + \integral_{0}^{0.1} x dx.
0.09 is the pr. of A falls in X if B falls in [0,0.9] and the integral is the
pr. of such event when B falls in [0.9,1]
【在 s*****n 的大作中提到】
: How to get this number, and why?
| s*****n
发帖数: 29 | 5 I didn't quite understand why these terms are compute in this way. Your
explaination seems involve some conditional probability. Can you explain more?
the
【在 s****m 的大作中提到】
: 0.1*0.9 + \integral_{0}^{0.1} x dx.
: 0.09 is the pr. of A falls in X if B falls in [0,0.9] and the integral is the
: pr. of such event when B falls in [0.9,1]
| D*******a
发帖数: 3688 | 6 P(A in X)=\int_0^1{P(A in X(B)|B=b)f(b)db}
=\int_0^0.9{0.1*1db}+\int_0.9^1{(1-b)db}
=0.09+0.005=0.095
more?
【在 s*****n 的大作中提到】
: I didn't quite understand why these terms are compute in this way. Your
: explaination seems involve some conditional probability. Can you explain more?
:
: the
| o*****1
发帖数: 4 | 7
The region meets the requirement would be in y = 1, x = 1, y = x and y = x + 0
.1
The size of the region is 1/2*1*1 (the big triangle) - 1/2 * 0.9 * 0.9 (The
small triangle) = 0.095.
【在 s*****n 的大作中提到】
: I didn't quite understand why these terms are compute in this way. Your
: explaination seems involve some conditional probability. Can you explain more?
:
: the
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