Recent content by ghostyc

Hi, I am writing a Matlab function(script), which take some input. I have several datasets in the workspace, say dataset1,dataset2,dataset3, ect In my function, I have tried to use data = input('Please input your dataset', 's') and then use 'data' as a variable for some computation, say...

Hi all, In this question, I found that \Pr(X_i|\theta)=\frac{\exp(\theta x_i)}{1+\exp(\theta)} and I carry on with the likelihood being \frac{\exp(\theta \sum x_i)}{(1+\exp(\theta))^n} and so s=\sum x_i = Tn I need some help with part (c)...

You are absolutely right. I was doing that for a long time and I got messed up with my integration. Now I have double checked with Maple. Thanks!

Hi there, Thank you for pointing the right direction. In fact. I have tried that already, f(x)=\int_0^x \mu \exp(-\mu s) \mu \exp(-\mu (x-s)) \, \mathrm{d} s =x\mu^2\exp(-\mu x) which is in the form of \mu (\mu x) \exp(-\mu x) , is something we would expect to get. Then I have some...

Hi all, I am now doing revision for one of the statistics module. I am having some difficulty to proove the following: Given n iid Exponential distribution with rate parameter \mu, using convolution to show that the sum of them is Erlang distribution with density f(x) = \mu...

I am now working on the bias is \bar{\theta}^{*} - \hat{\theta} = \frac{1}{n} \sum_{i=1}^n (y_i^* - \bar{y} )^2 - \frac{1}{n} \sum_{i=1}^n (y_i - \bar{y} )^2 after some munipulation , i got to \frac{1}{n} \sum_{i=1}^n \left( {y_i^*}^2 - y_i^2 -2\bar{y} (y_i^*+y_i) \right)...

slowly giving up on this one

i will look into it again sometimes, i really get confused what i am looking for

Hi there, I finally see something here. Is there any possibility that the 'red' part is referering to the pivotal interval? Thanks. I am a bit desperate now.

Hi, Can someone kindly explain a bit on the 'red' part. I have tried to search for it, but nothing much related seem to come out. You may not tell me what it is, all I need is some related resource ( section in a book, or a website, or an article? ) Thanks.

http://img138.imageshack.us/img138/6060/98259799.jpg I have done part one and found that the bias is \frac{\theta}{n} then i don't know how to proceed. in my notes, have the following result, http://img189.imageshack.us/img189/9699/resultc.jpg i am thinking, this time i have to...

at last, i think i got it \operatorname{E}(\hat{\theta})=\frac{1}{n}\left(\sum_{i=1}^n \theta - n\frac{\theta}{n} \right)=\frac{1}{n}(n\theta-\theta)=\theta-\frac{\theta}{n} \quad \implies \quad \operatorname{Bias}(\hat{\theta})=\operatorname{E}(\hat{\theta})-\theta=\frac{\theta}{n}

That's what I did so far. But I just can't use the memoryless property to do it ... http://img138.imageshack.us/img138/5945/tempz.jpg

\Pr(T > s + t\; |\; T > s) = \Pr(T > t) \;\; \hbox{for all}\ s, t \ge 0. i just can't convert from expectation to the probability... damn

Given X follows an exponential distribution \theta how could i show something like \operatorname{E}(X|X \geq \tau)=\tau+\frac 1 \theta ? i have get the idea of using Memorylessness property here, but how can i combine the probabilty with the expectation? thanks. casper