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#1 Re: Help Me ! » a probability question. » 2016-05-12 04:51:19
Hi thickhead:
fantastic answer. many thanks.
I still have no idea about (e),how to estimate P(0.8<X+Y<0.801)?
#2 Help Me ! » a probability question. » 2016-05-11 04:57:11
- ChrIsPuZa
- Replies: 10
suppose random variables X and Y has joint pdf f(x,y)=k-y 0<y<x^2<1
a) find k
b) find marginal pdf f(x) and the conditional pdf f(x|1/2) and cdf F(y|1/2);
c) find P(X<Y|Y>1/2), E(X|1/2) and E(X|Y>1/2)
d) what's the correlation between X and Y?
e) find the value of pdf of U=X+Y evaluated at u=0.8 and estimate P(0.8<X+Y<0.801)
Any help here would be greatly appreciated!
#3 Re: Help Me ! » A statistics question need help. » 2016-05-04 16:47:11
Hi bobbym:
do you have any idea about (d)? which method will not involve any differentiation to find mean and variance?
#4 Re: Help Me ! » A statistics question need help. » 2016-05-04 16:19:19
thanks anyway
#5 Re: Help Me ! » A statistics question need help. » 2016-05-04 05:35:12
you are right, i make a mistake here . I have no idea about the second part question
'express the first and second derivative of r(0) in terms of E(W) and Var(W)'
#6 Re: Help Me ! » A statistics question need help. » 2016-05-04 04:54:23
Hi:
sorry about that ,I don't know why there are some box appeared in your browser.
you can ignore these box ,the question is find the first and second derivative of r(t) and express the first and second derivative of r(0) in terms of E(W) and Var(W)
#7 Re: Help Me ! » A statistics question need help. » 2016-05-04 02:28:20
Hi bobbym:
I'm also confused about (b) ,but I don't think there are missing characters. shall we consider about this :
r(t) = logm(t) , r'(t)=m'(t)/m(t) r''(t)=[m''(t) m(t)+(m'(t))^2] / (m(t))^2
and then we find r'(0)=m'(0) / m(0) =EW/m(0) .does this idea correct ? but how to use the EW and VarW to eliminate m(0)? thank you for your reply
#8 Help Me ! » A statistics question need help. » 2016-05-03 06:15:46
- ChrIsPuZa
- Replies: 11
Suppose a rv Y has mgf m(t)=e^[k(e^t -1)] / (1-bt)^a
a) obtain the mean and variance of Y (differentiate this mgt twice)
b)Suppose m(t) is the mgf of a rv W. Let r(t) be the natural logarithm of m(t),
i.e. r(t) = logm(t). Find r'(t) and r''(t) , and express r'(0) and r''(0)in terms of EW and VarW.
c) Use the result in (b) to find the mean and variance of the rv Y in (a)
d)Find the mean and variance of the rv Y in (a) using a method which does not involve any differentiation.
really difficult for me
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