Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose there are n i.i.d exponential random variables Yi, i=1,2...n and another random variable X independent of Yi, i=1,2...n.
The cumulative probability distribution function of X is
$$F(x)=\left\{\begin{matrix} (1-e^{-2x})^{n} &x\geq 0 \\ 0&x<0 \end{matrix}\right.$$ The probability density function of Yi is
$$f(y)=\left\{\begin{matrix} e^{-y} &y\geq 0 \\ 0&y<0 \end{matrix}\right.$$ Let S be a set of Yi s satisfying Yi < t.Thus the size of S is a binomial random variable which may not be independent of those Yi s belonging to S .
$$\left | S \right |\sim B(n,1-e^{-t})$$ Now what is the result of the probability $$ P\left ( \frac{X}{b+\sum_{j\in S}Yj}<c \right ) $$ where b and c are both positive constants? Or is it less than some value or expression?

share|improve this question
    
$Xi$ >> $X$? $ $ –  Did Feb 4 '13 at 15:35
    
sorry,it should be X. –  yyzhang Feb 5 '13 at 0:53
    
There is no reason to expect anything simpler than the multi-dimensional integral one is thinking about. –  Did Feb 7 '13 at 13:09

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.