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Yes, I know your logic. But I found the marginal expression today. I put it here. I wanna know is it correct, or under what condition I can get F(x) that way?

If there are X and Y two random variables. The pdf of Y is f(y), and conditional pdf of X is f(x|y). I want to find the marginal CDF of X, the F(x). Is this correct? F(x)=\int^{F(x|y)}_{-\infty}f(y)dy \dfrac{d}{dx}\int^{F(x|y)}_{-\infty}f(y)dy=\int^{\infty}_{-\infty}f(x|y)f(y)dy=f(x)?

(X_1^2+X_2^2)/(X_1-X_2)^2 is a non-central F random variable. But the non-central parameter is unknown.

I don't know if this is possible or not, let's see if this is a fun problem. Let X_1 and X_2 be 2 independent normal random variables. They have different means and variances, and they are independent. I want to have a function that inputs X_1 and X_2, and it has a F distribution with degree of...

For a simple linear model: \alpha+\beta\times x=y If it is observed that y \in (-8.51,23.20) given x=4 The question is to give intervals of \alpha, \beta, which satisfy y \in (-8.51,23.20) given x=4. Is this problem identifiable? Can it be found the unique intervals for \alpha...

Hi all: The inequality here involves abs, and max functions, how to solve for the interval as show below?

Say, I'm a bookkeeper of a gamble of flip coin. The price for each trial is 0.5, i.e. if there is a head I pay gambler 0.5, otherwise I get 0.5 from the gambler. There are only 10 flips or trials in the game, so that each gamble only can play 10 trials. I know to choose the 0.5 as the fair...

Hi all, I want to learn Game-Theoretic Probability. I have found few examples of computing conditional probability by game theoretic approach. Is there and good readable tutorial could show help me to learn this topic and conformal predictions? Let's recover this lost philosophy of...

Why does Ʃ1/n4 not diverges? I have BS in biology, now I working with probability, only can troubleshoot math with you guys. Thanks

\sum_{m=1}^N(\frac{1}{m^4}-\frac{1}{m^6}) My math on sum series is very rusty, can anyone show me show this sum converges? It is not geometric series, right? Suddenly found out it is needed to show Kolmogorov SLLN of some random varianble. Thanks in advance

The compressed R packages have file extension .tar, they are called tar balls. If you open the tar balls, you can see all sources codes are ASCII text files.

Variables x, y, z, in algebra, are place holders. q(y,x)=normal(0,1) means y=0 x=1 Algebra is a incomplete story of placeholders. Be careful where you can plugin the values.

R is open source right? Please read the source code from the package

You can look at R package http://cran.r-project.org/web/packages/copula/index.html

Copula is just a joint probability distribution. The beauty is that copula models correlation. The downside is it is difficult to formulate different couplas. I like baysian network modelling of joint distributions. Baysian network handles more variables, not only bivariates; the downside is...

Fourier transform

I guess the jump discontinuous functions are not random variables.

There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables. If you know functions are not random variables please please reply this post. This class is about set theory, probability measure, Borel...

Hi all: The Heaviside function multiples a random varaible, is that a probability density function? This is my first time knowing about Heaviside, any tutorial and application of it?

Yes, I should stated more clearly. How to do the covariance of the estimators? I use too much simulation methods, this kind exact formulation I did not work with before.

There are 2 parameters in the Gamma distribution, alpha and beta. If sample 500 of the Gamma random variable, there unbiased mean and variance can be estimated by the sample moments. If it is also interested to estimate the variance and covariance of the parameters, alpha and beta; Jacobian...

Guys, I'm taking real analysis starting with open, close, compact sets, and neighborhoods. Now I'm addict to rely on these concepts to do my proofs. In the future I will have to take Measure Theory. Can anyone give me a percentage indication for how many percent theorems are proven by the set...

Linear Spaces Norms and inner products Holder’s inequality Minkowski’s inequality Normed linear spaces Cauchy sequences and complete spaces Banach spaces Reitz representation theorem Hilbert spaces Orthogonal bases Generalized Fourier expansions Lebesgue Measure and...

The implications of Heine Borel Thm are not immediate to me. Any results are derived from this theorem?

Hi all, It has been very useful of posting my questions here to help me pushing through the book reading of analysis. This forum is a perfect place and the best place for people who are interested in knowledge and the beauty of knowledge. Here goes another question from me. All continuous...

They should call Heine-Borel a lemma, not theorem. Theorem can be used to derive quantities. Lemma is for proving theorems.

Hello all: Closed interval subcover is finite. How do I use it? Why should anyone on earth proved things like this? Please give me the significance of this technological development. Thanks, zli034

I would like to continue this Question & Answer because the new confusions. From the book I'm reading that set Q is an Archimedean Ordered Field. However set R of real number will obey all the axioms for Archimedean Ordered Field together with one more axiom, called the Completeness Axiom...

How cool is that! I counted there are 4 addition properties, 5 multiplication properties. Let's call the order, 10th property.

Could anyone explain me the concept of Ordered Field? I have googled it, all came up are definitions I don't know how to handle. Numbers and calculations with statistical means I can understand fairly simple; but pure math has never worked for me. Can anyone make the ordered field with...